SCED 647 Unit Plan - Merged

Triangles: Properties, Attributes, and Congruence
Jeremy Sierakowski
Unit Plan Overview and Description

Geometry is a course that many people think is all (or only) about shapes. Many would be surprised to realize
that there are 11 units in the Baltimore County Geometry Curriculum and the first unit to focus on shapes is the
fifth unit. That shape is the triangle. It is the most basic of shapes because it has the minimum amount of sides
to create a polygon. Without at least three sides, a shape cannot be constructed. With that being said, its basic
nature has a lot of interesting features that create the basis of our understanding for all other polygons. I chose
this topic because triangles are a topic that is necessary knowledge for later in students’ high school career.
Geometry is the black sheep of math classes in high school because it is wedged in between Algebra 1 and
Algebra 2 and is completely different than the two. The enduring learning that is necessary for later classes is all
about triangles when students get to Trigonometry. This unit is planned for my 9th and 10th grade students in
Standard Geometry. These are some of the lower achieving students in my school and my classes usually have
many 504 and IEP cases.
The instructional strategies used throughout this unit are made so students have a choice. Students can choose
how they take notes, they can choose the pace they learn, or they can choose the difficulty of work that fits
them. Most lessons require students to take measurements and discover characteristics and properties of
triangles through inquiry. The higher achieving students can complete as much as they want on their own, while
those who are less mathematically inclined can follow at their pace and be reassured of their findings when the
teacher goes over results as a class. The activities are designed as much as possible to accommodate
translanguaging in a math class by giving students the option of how they take notes and express themselves.
The activities also are evident of a maker-centered learning environment where students are constructing their
knowledge by drawing the shapes and taking measurements themselves.
Common Core State Standards

• HSG-CO.B.07 - Use the definition of congruence in terms of rigid motions to show that two triangles
are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are
congruent. segment; and constructing a line parallel to a given line through a point not on the line.
• HSG-CO.B.08 - Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the
definition of congruence in terms of rigid motions.
• HSG-CO.C.10 - Prove theorems about triangles. Theorems include: measures of interior angles of a
triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of
two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a
point.
• HSG-MG.A.03 - Apply geometric methods to solve design problems (e.g., designing an object or
structure to satisfy physical constraints or minimize cost; working with typographic grid systems based
on ratios).
• HSG-SRT.B.05 - Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
• HSG-SRT.B.04 - Prove theorems about triangles. Theorems include: a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using
triangle similarity.
• HSG-SRT.C.06 - Understand that by similarity, side ratios in right triangles are properties of the angles
in the triangle, leading to definitions of trigonometric ratios for acute angles.
• HSG-SRT.C.08 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
applied problems.
Objectives
1. Students will be able to identify triangle congruence given a diagram or list of measurements.
2. Students will be able to analyze, plan, and construct proofs in order to prove that triangles are congruent
to each other.
3. Students will be able to discover and formalize theorems pertaining to triangles.
4. Students will be able to use triangle theorems to solve real world problems.
Formal Assessments
1. Triangle Congruence Quiz
2. Triangles Unit Test
Informal Assessments
1. Exit Tickets will be given on many days throughout the unit.
2. Homework Completion/Attempts will be graded.
Unit Calendar
Week 1 Monday Day 1 Tuesday Wednesday Day 2 Thursday Friday Day 3

Objective: Students will Objective: Students will Objective: Students will be
be able to classify be able to use properties able to apply SSS and SAS
triangles by their angle of congruent triangles in to construct triangles and
measures and side order to prove that prove that triangles are
lengths, use triangle triangles are congruent congruent.
classification to find based on the definition of Standard: HSG-CO.B.07
angle measures and congruence. HSG-CO.B.08
side lengths, and find Standard: HSG-CO.B.07 HSG-SRT.B.05
the measures of interior HSG-CO.B.08 Activity: Students will go
and exterior angles of HSG-SRT.B.05 through construction
triangles. Activity: Students will activities to show that with if
Standard: HSG- first learn what it means two triangles have the same
CO.C.10 to be congruent. (All measurements for their
Activity: 1. Students sides and angles must be sides, the angles will
will take notes on equal between two automatically be congruent.
triangle vocabulary. different shapes). Then They will also go through a
Students will be able to students will go through construction to show that
use any note taking many examples of proofs two sides and the included
strategy they would like to prove that triangles are angle will create two
based on the congruent. Proofs will triangles that are congruent.
information given in start easier and get harder This is helpful because the
the PowerPoint. They through the class. proofs can be shortened
can take notes by Students will be able to because the number of
drawing pictures, decide by the end of class pieces to prove are
writing down what level they are at of congruent is cut in half.
characteristics of each proof. Proofs that will be
term, or any other provided for students can Students will then practice
method that works for be pre-constructed with identifying which
them. some pieces missing. congruence postulate to use
Some can have word (SSS or SAS) and then
2. Students will make banks. Or students can constructing the proof using
measurements of many decide that they want to learnings from the previous
different triangles that construct the proof from class.
have different “shapes” scratch which would be Assessment:
and sizes. Students will the hardest level proof. SSS and SAS Homework
find with their Assessment:
protractors that the Exit Ticket on Triangle 2
interior angles will add column proofs.
up to 180 degrees every
time. After that students
will complete a proof
that shows that the
exterior angles will add
to 360 no matter the
shape.
Assessment: Exit
Ticket on triangle
classification and
measurements.
Week 2 Monday Tuesday Day 4 Wednesday Thursday Day 5 Friday
Objective: Students will be Objective: Students will be able to use
able to use ASA, AAS, and CPCTC to prove that parts of
HL to construct triangles and congruent triangles are congruent.
prove that triangles are Standard: HSG-MG.A.03
congruent. HSG-SRT.B.05
Standard: HSG-CO.B.07 Activity:
HSG-CO.B.08 This will serve as more of a practice
HSG-SRT.B.05 day for proofs. CPCTC is an extra step
Activity: Students will learn in the proofs students have been
about three other congruence working on. They need to complete the
postulates. Since there are five proofs as they have been for the past
different postulates student few classes and then at the end add a
swill need time to practice step to say a specific part of the
identifying which one applies triangles is congruent. By the end of
to different diagrams. Students this class, students should be able to
need a lot of practice on this complete proofs from scratch.
before doing the proofs Assessment:
because the diagrams are Exit Ticket on 2 column proofs
difficult to dissect and involving triangle congruence and
understand fully. CPCTC
Once students have practice on

identifying the congruence
postulate to use. They can then
get practice on completing
proofs. Sometimes the hardest
part of completing the proof is
starting it because students do
not know what their plan is
going to be.
Assessment: Exit Ticket on
identifying congruence
postulates from diagrams of
triangles
be able to use theorems be able to demonstrate able to prove and apply
of isosceles and their proficiency with theorems about
equilateral triangles to triangle congruence by perpendicular and angle
complete proofs and completing the bisectors.
solve for measurements congruence assessment. Standard: HSG-CO.C.10
of those triangles. Standard: All previous Activity: Students will go
Standard: HSG- standards over the quiz from the
CO.C.10 Activity: Students will previous class and get
Activity: Students will participate in a last questions answered about
be given isosceles and minute review session. things they may have gotten
equilateral triangles and Teacher will take wrong.
be instructed to make questions on the review
measurements for the packet given for Students will have a quick
sides and angles. homework the class intro to the second part of
Students will be able to period before. the triangle unit. Students
discover the properties Assessment: Triangle will construct perpendicular
of these triangles easily Congruence Quiz and angle bisectors in
through these triangles and will take
measurements. measurements using a ruler
After the discovery, and protractor. Students will
teacher will bring class discover properties
together to formalize associated with these
the findings and bisectors and use the
vocabulary. properties to solve problems
After theorems are both “real” and algebra-
formalized, students based.
will practice solving Assessment: Homework
problems that feature completion on bisectors.
real world
measurements and
algebraic practice.
Assessment: Exit
Ticket on Isosceles and
Equilateral Triangles
Objective: Students will be able Objective: Students will be able to
to prove and apply the triangle use the triangle inequality theorem to
midsegment theorem. practice constructing indirect proofs.
Standard: HSG-CO.C.10 Standard: HSG-CO.C.10
Activity: Students will learn Activity: Students will measure the
what a midsegment of a triangle angles and sides of a triangle that
is and construct one on a triangle they make. In an open ended
tha they make. They will learn activity, they will be tasked with
that it is parallel to one side of finding a way to find a relationship
the triangle and also half the between the sides and angles. This is
length of that side. Students will particularly tough because their
then solve problems that deal triangle could be very different from
with perimeter and algebraic their neighbor. They need to think
expressions that will challenge very abstractly and look at the
students to mix their fundamentals of these numbers. If
interpretation of the diagrams my leading questions are good
and their proficiency with enough while I circulate through the
solving algebraic equations. groups, they should be able to find
Assessment: Exit Ticket on that the largest side is across from
Triangle Midsegment Theorem the largest angle and the shortest side
is across from the smallest angle.
This relationship seems basic but
will be important for students as a
logic check for the rest of the course
as well as in trigonometry. This
fundamental idea can help student
avoid a lot of mistakes later in their
math career with triangles.
Assessment: Homework on triangle
inequalities.
be able to the be able to justify and able to justify and apply
Pythagorean Theorem apply the properties of properties of 30-60-90
to solve measurements 45-45-90 triangles. triangles.
for right triangles and Standard: HSG- Standard: HSG-SRT.C.06
use Pythagorean SRT.C.06 Activity: Teacher will
inequalities to classify Activity: Students will review the 45-45-90 triangle
triangles. need to review how to pattern and show students
Standard: HSG- simplify radicals and the pattern for the 30-60-90
SRT.B.04 rationalize a fraction triangle. Students will be
HSG-SRT.C.08 when the denominator given time to practice
Activity: Students will has a radical. memorizing the pattern and
be given a real world using it to solve for missing
problem where the Once students are side lengths on these special
teacher needs to buy a comfortable with this right triangles. The skill
tv that fits in a space skill, teacher can seems easy at a glance, but it
above a fireplace. The introduce the 45-45-90 takes students a while to get
teacher needs to know triangle by using the comfortable with and learn
how much height space characteristics of how to use the pattern, so a
they will have for the tv isosceles triangles with lot of practice and
given the measurement. different leg collaboration time should be
TVs are measured measurements. Students given.
diagonally across their will see that there is a
screens so students will pattern that arises with Assessment:
need to learn about the side lengths that will Exit Ticket on special right
Pythagorean theorem to allow them to solve triangle measurements
solve for missing sides problems without the
of the TV. Pythagorean Theorem.
After this real world Assessment:

problem, students will Homework on 45-45-90
practice their skills triangles
without a calculator and
by simplifying radicals
(a skill learned in
Algebra 1 but will need
to be revisited).
Assessment: Exit
Ticket on Pythagorean
Theorem
Objective: Students will be able Objective: Students will be able to
to use the properties of special demonstrate their proficiency with
right triangles to identify Triangles by completing the Unit
trigonometric ratios in right Test
triangles. Standard: All previous standards
Standard: HSG-SRT.C.06 Activity: Triangle Unit Test (90
Activity: This is a bonus lesson Min)
that will help students for the Assessment: Triangle Unit Test
next unit which is Trigonometry.
Special right triangles make up
the bulk of the beginning of
trigonometry classes so this extra
practice will go a long way.
Students will use these special
right triangles as a basic
introduction to sine cosine and
tangent and how they are related
in The Unit Circle. Tying these
concepts together will give
students a more solid
understanding in the
trigonometry unit as well as in
their eventual trigonometry
class.
Assessment: Homework on sine,
cosine, and tangent.
Appendix A
Course Name: Geometry Unit Plan Day: DAY 1
1, 3, 8, etc.
Level Standard Lesson Duration: 90 minutes

(Grade/Honors/AP How many minutes
) will this lesson last?
(Lesson should last at
least 45 minutes)
Lesson Objective:
• At the end of the lesson, my students will understand how to classify different types of triangles according to their
sides and angles as well as learn that all those triangles’ interior angles add to 180° and exterior angles add to 360°.
Standard Alignment (state and national):

Only list one or two
HSG-CO.C.10 - Prove theorems about triangles. Theorems include: measures of interior angles of a
triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of
two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a
point.
SUMMARY OF TEACHING TASKS/ACTIONS:

Include a description of the lesson activities, clarifying: 1) what the student will be doing, 2) what the teacher will be
doing. and 3) how long the specific activity should take.
Estimated Time: Teacher Does: Students Do:

[i.e. 5 minutes, 7 This section should describe what the What are the students doing during this time?
minutes] teacher is doing or saying to guide student What activities are they engaged with? Are they
understanding. Include at least three quotes working independently or in groups?
of what a teacher would say to guide the
mini-lesson or lesson plan.
5 minutes Teacher will give students a warm up Students should answer warm up questions
reviewing previously learned vocabulary. and access prior knowledge to be ready for the
Say: “I want you to think of these words lesson ahead.
and what they mean while we learn new
vocabulary this lesson. We may be able to
come up with definitions on our own based
on what we already know.”
20 minutes Teacher will go through the slides that Students should be taking notes however they
cover all different types of triangle types. want to make it easier on themselves.
These are categorized by sides or angles.
The types of triangles included are: Acute,
Obtuse, Right, Equiangular, Scalene,
Isosceles, and Equilateral. Teacher should
say, “I encourage you to take these notes
however you would like. You can either
draw a picture, write a brief definition, or
combine both efforts. Whatever works for
you.” Allowing students to take notes there
own way will allow them to be able to
better understand and read later when they
are studying.
20 minutes Teacher will give students time to practice Students will complete the classwork paper in
and use their new knowledge by small groups. They can work in small groups
completing the classwork sheet. Students since this is new material and they can bounce
will have to identify types of triangles ideas off each other.
while also solving for certain
measurements in triangles given the
information that they just learned.
20 minutes Teacher will hand out rulers and Students will make triangles and measure the
protractors to students. Teacher will appropriate parts. They should be focused on
instruct students to make a triangle using clean and organized work and measuring
the ruler as a straight edge. The triangle precisely, which is an important skill in
can be any size or orientation. Once all Geometry.
students have made their triangle the
teacher should instruct everyone to
measure all of the interior angles. When
the students share out, they will find that
everyone has the same measurement, 180°.
Teacher should say, “Please be sure to
make accurate measurements. Even if you
are only off 1 degree, that could make a
big difference for your findings later.”
10 minutes Teacher will lead students through a proof Students will follow along with teacher’s
of the exterior angle theorem. Interestingly instructions to be able to measure their
enough, all the exterior angles of the triangle’s exterior angles.
triangle will always add up to 360°.
15 minutes Teacher will give students an exit ticket on Students take the Exit Ticket.
all topics covered. How students do on this
will allow teacher to understand if students
are understanding and ready to move on or
if a concept needs to be re-explained next
class.
MATERIALS/EQUIPMENT:
What materials or equipment is needed to support this lesson?
Classifying Triangles Slide Show

Classifying Triangles Classwork
Ruler
Protractor
Exit Ticket
JUSTIFICATION:
In this section, specifically describe how you integrated contemporary instructional methods that we’ve discussed in
this class to support diverse groups of student learners. Please visit our course syllabus to ensure that you address
methods and concepts from each area of our class study. Cite your resources and include them in the “References”
section below.
This section should be no longer than 1/2-page, single-spaced.
During the notetaking portion of this lesson, I am implementing strategies from Fu’s “Translanguaging for
Emergent Bilinguals”. In the book, teachers are encouraged to let students take notes in whatever language they
want. It is noted that students may speak in English, but think in Spanish or students can write faster in a different
language. On page 49, an anecdote from a math class shows Rodrigo writing notes in Spanish with some English
terms because he can write faster, he can connect the material to previous learning in his home country, and he is
the only audience for the notes. I am doing a similar thing by allowing students to write their vocab notes however
they like. If they want to write the English definition they can, if they want to paraphrase for themselves they can,
a different language is also fine. I go a step further by letting them draw pictures for notes. Math is a language in
itself in my eyes, so if students want their notes to be more math based than word based, then I allow it.
REFERENCES:
Please include the correct APA citations for each of the resources cited above.
Fu, D., Hadjioannou, X., Zhou, X. (2019). Translanguaging for emergent bilinguals: Inclusive teaching inthe
linguistically diverse classroom.
4-1 Classifying Triangles
Warm Up
Classify each angle as acute, obtuse, or right.
1. 2.
3.
4. If the perimeter is 47, find x and the lengths

of the three sides.
Holt McDougal Geometry

Objectives
Classify triangles by their angle measures
and side lengths.
Use triangle classification to find angle
measures and side lengths.

Vocabulary
acute triangle
equiangular triangle
right triangle
obtuse triangle
equilateral triangle
isosceles triangle
scalene triangle

Recall that a triangle ( ) is a polygon

with three sides. Triangles can be
classified in two ways: by their angle
measures or by their side lengths.

C
A
B
AB, BC, and AC are the sides of ABC.
A, B, C are the triangle's vertices.

Triangle Classification By Angle Measures
Acute Triangle
Three acute angles

Equiangular Triangle
Three congruent acute angles

Right Triangle
One right angle

Obtuse Triangle
One obtuse angle

Triangle Classification By Side Lengths
Equilateral Triangle
Three congruent sides

Isosceles Triangle
At least two congruent sides

Scalene Triangle
No congruent sides

Check It Out! Example 1
Classify FHG by its angle measures.
EHG is a right angle. Therefore mEHF +mFHG = 90°.

By substitution, 30°+ mFHG = 90°. So mFHG = 60°.
FHG is an equiangular triangle by definition.

Check It Out! Example 2
Classify ACD by its side lengths.
From the figure, . So AC = 15, and ACD is

scalene.

Classifying Triangle Classwork Name:
1. Given the figure below, classify the following triangles by their angle measures.
• △ BDC
• △ ABD
• △ ADC
2. Given the figure below, classify the following triangles by their side lengths.
• △ EHF
• △ EHG
• △ FHG
3. Find the side lengths of △ JKL.

4. Find the side lengths of equilateral △ FGH.
5. A steel mill produces roof supports by welding pieces of steel beams into equilateral triangles. Each side of the
triangle is 18 feet long. How many triangles can be formed from 420 feet of steel beam?
Intro to Triangles Exit Ticket Name:
Classify each triangle by its angles and sides.
1. △ MNQ
2. △ NQP
3. △ MNP
4. Find the side lengths of the triangle.
5. Find the indicated angle measurement.

6. Find m∠WST.
7. Find m∠A.
Appendix B
1, 3, 8, etc.

least 45 minutes)
Lesson Objective:
• At the end of the lesson, my students will understand how to use the Triangle Midsegment Theorem to solve for
missing measurements in triangles.

HSG-CO.C.10 - Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum
to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle
is parallel to the third side and half the length; the medians of a triangle meet at a point.


10 minutes Teacher will give students a review warm Students will complete warm up. They can
up on formulas from earlier in the year that work in pairs around them and can use prior
they will use during this lesson. (i.e. notes for help. The purpose of this is so they
Midpoint Formula, Distance Formula, are ready to use the formulas during class.
Slope Formula).
20 minutes Teacher will give students the discovery Students will complete a discovery activity
activity. Teacher should implore for made by the teacher. The activity will have
students to, “Be careful when using the students plot a triangle on a coordinate grid
formulas. If a mistake is made the and use the formulas to find the mid points of
measurements will not make much sense two sides and measure certain lengths and
for the problem. Make sure that the slopes of sides. High achieving students will
numbers seem logical when done using the be able to extrapolate the theorem from these
formulas.” findings.
10 minutes Teacher will bring students back together Students should follow along and take notes.
to debrief on the findings. The class should Hopefully they are able to answer teacher
be able to agree that the midsegment is half questions regarding corresponding angles and
the length of the side of the triangle that it alternate interior angles.
is parallel to. Teacher should bring up prior
information to help students come to this
conclusion. “What does it mean when
these corresponding angles are
congruent?”
35 minutes Teacher will allow students time to Students will practice their new skills by
practice with this new theorem. Problems completing the practice worksheet. They
can span from very basic to difficult. should consult their peers and ask questions to
Teacher should focus on problems that the teacher while the teacher circulates the
have an algebra base. Setting up these room.
problems can be rather confusing and
students tend to get mixed up when either
doubling the midsegment or cutting the
side of the triangle in half to solve the
algebraic equation. Teacher should remind
students “Make sure you are not cutting
the smaller length in half. That has to be
doubled in order to make it equal to the
side that is twice its size.” Teacher will go
over the answers for the practice problems,
so students have feedback before they take
the assignment
15 minutes Teacher will give students the Exit Ticket Students take the exit ticket on the Triangle
Midsegment Theorem
Triangle Midsegment Theorem Warm Up

Triangle Midsegment Discovery Paper
Triangle Midsegment Practice Worksheet
Triangle Midsegment Theorem Exit Ticket
JUSTIFICATION:
section below.
This lesson features aspects of a maker-centered classroom. Rather than telling students all the information from
the start and getting right into practice of the concept. I am having students follow instructions to create a triangle
and do measurements on their own to hopefully find and create the knowledge that is described in the theorem. If
I just give them the information in the beginning, they do not care about the concept. If they see the results of the
theorem in front of them before they even know it is a theorem, the concept becomes more concrete and they are
more engaged in the learning. This is highlighted in “Maker Centered Learning” when talking about
Constructivism. “Constructivism, a view developed by mathematician and educator Seymour Papert, holds that
learning happens best when learners work directly with manipulable media.” ( Clapp et al., 2017, p. 46). In a
perfect world, I could tell my students to make their own triangle, and make the measurements with a ruler, but
my students need a lot more structure due to their problem solving skills and previous learning. I still argue my
activity is a maker-centered activity even with its scaffolding because my students are constructing the knowledge
themselves without me giving them answers.
REFERENCES:
Clapp, E. P.; Ross, J.; Ryan, J. O.; Tishman, S. (2017). Maker-centered learning: Empowering young people to
shape their worlds. Jossey-Bass.
𝑥1 +𝑥2 𝑦1 +𝑦2 𝑦 −𝑦
Midpoint Formula: ( 2
, 2 ) Slope Formula: 𝑥2 −𝑥1
2 1
Distance Formula: √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Use the points A(2, 2), B(12, 2) and C(4, 8) for 1–5.
1. Find X and Y, the midpoints of AC and CB.
2. Find the length of XY.
3. Find the length of AB.
4. Find the slope of AB.
5. Find the slope of XY.

𝑥1 +𝑥2 𝑦1 +𝑦2 𝑦2 −𝑦1
Midpoint Formula: ( , ) Slope Formula:
2 2 𝑥2 −𝑥1
Distance Formula: √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Use the points A(2, 2), B(12, 2) and C(4, 8) for 1–5.
1. Find X and Y, the midpoints of AC and CB.
2. Find the length of XY.
3. Find the length of AB.
4. Find the slope of AB.
5. Find the slope of XY.

Triangle Midsegment Theorem Discovery Name:
The vertices of ∆XYZ are X(–1, 8), Y(9, 2), and Z(3, –4). M and N are the midpoints of XZ and YZ.
1 Plot the vertices of △ XYZ on the coordinate grid above.
2. Find the coordinates of M and N using the Midpoint Formula.
3. Compare the slopes of ̅̅̅̅̅ ̅̅̅̅̅

𝑀𝑁 and 𝑋𝑌.
4. Compare the lengths of ̅̅̅̅̅

𝑀𝑁 𝑎𝑛𝑑 ̅̅̅̅̅
𝑋𝑌.
Triangle Midsegment Theorem Practice Name:
1) If 𝐴𝐵 = 20, then 𝑌𝑍 = ______
2) If 𝐶𝑌 = 8, then 𝑋𝑍 =______
3) ̅̅̅̅
𝑋𝑌 ∥____
4) If m∠ABC = 33°, then m∠YZC =
5) XZ = 3, XY = 5, and YZ = 4. What is the perimeter of ∆ABC?
6) Solve for x. AC = x + 9 and XZ = 2x − 3

7) Find YZ and AB.
𝐴𝐵 = 𝑥 + 2
𝑌𝑍 = 2𝑥 − 14
8) Solve for x.
𝑚∠𝐵𝐴𝐶 = 42°
𝑚∠𝑍𝑌𝐶 = 3𝑥 + 27
Triangle Midsegment Theorem ET Name:
Use the diagram on the right to answer 1-3. Find each measure.
1) ED
2) AB
3) 𝑚∠𝐵𝐹𝐸
4) Find n.
5) What is the perimeter of ∆XYZ.

Appendix C
1, 3, 8, etc.

least 45 minutes)
Lesson Objective:
• At the end of the lesson, my students will understand how to use the Pythagorean Theorem to solve real world
problems.

HSG-SRT.B.04 - Prove theorems about triangles. Theorems include: a line parallel to

one side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.
• HSG-SRT.C.08 - Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.


10 minutes Teacher will set students up with a Students will listen and try to piece together
motivational activity. My students know I the information tha tI need to find the right
like to play videogames and that I recently TV. Students should realize they need to know
bought a house. I am in the process of about the space provided and how the TV is
buying many pieces of furniture and other measured.
amenities which include a TV. I know
where in the house I want to put a TV, I
just do not know the size that will fit. TVs
are sold by the diagonal length of their
screen, so I need to find the other
dimensions of the TV. Teacher should say,
“I am relying on your guys work to make
the right purchase. Without this work I
could get a TV that is way to big for the
space and then I will have to return it and
get another one which would be
annoying.” Selling the situation really
drives the purpose of learning this
material.
40 minutes Teacher will let the students know there is Students will takes notes and practice the new
a way to find out the information, but theorem in small groups. They will have to be
before I trust them with picking a TV size, careful using their calculators and taking the
we need to know exactly how this way square root or squaring numbers. It is easy for
works. students to come up with wrong answers even
when they have a strict formula to follow.
Teacher introduces the Pythagorean
Theorem and does a quick proof of it from
a computer software.
Teacher then will lead students through

examples of how to use the Pythagorean
Theorem and allow students time to
practice on their own.
Teacher should make it clear to students

that they will have to substitute
information into the formula differently for
different sides they are looking for. A
hypotenuse is different than a leg in this
case. Teacher should say, “Make sure you
know whether you are solving for a, b, or c
in the formula. C is always the hypotenuse,
so if you are already provided that
measurement, make sure that is substituted
for C.
25 minutes Teacher will then have students work on Students will have to research the TV
the TV problem. Students will need to dimensions and use Pythagorean theorem to
research the dimensions of a TV since they see what TV size will fit in the space I provide
all have the same picture dimensions. That them from my house.
will allow them to find how tall a certain
TV will be and if it will fit in the space I
want in my house.
15 minutes Teacher will give students an Exit Ticket Students will take the Exit Ticket.
to see if they can solve for different side
lengths of a right triangle
Pythagorean Theorem Motivation Slides

Pythagorean Theorem Practice Worksheet
Pythagorean Theorem Exit Ticket
Calculator
JUSTIFICATION:
section below.
This lesson is one of my favorites because it is one of the best examples of student engagement when it is done
correctly. I use some ideas from Better Than Carrots or Sticks in this lesson. One being fostering the relationship
with my students. As motivation for the learning I am setting up a scenario where I am relying on the class for
help. I am acting like without them I cannot solve this problem. I am giving them empowerment for their work. I
am also using real pictures from my house so I am letting them in on my life and trusting them with that. When
talking about collaborative learning, the number one thing mentioned is a meaningful and complex task. The task
I have for students in this lesson seems very easy on the surface but actually involves a lot of measuring and
researching to be confident with an answer. Something like this will allow students to feel like they are
accomplishing something with their learning and they can see how it feels to really solve a problem that could
come up in the real world that seems mundane but is actually complicated.
REFERENCES:
Smith, D., Fisher, D., & Frey, N. (2015). Better Than Carrots or Sticks: Restorative Practices for Positive
Classroom Management. ASCD.
How big of a TV can Mr. S buy?
Pythagorean
Theorem
• a and b are always the legs

• c is always the hypotenuse
Pythagorean Theorem Practice Worksheet Name:
Find the missing side of the triangle in the simplest radical form. No calculator.
1. 2.
6
6
√𝟕𝟐
3. 4.
√𝟐 √𝟏𝟔𝟎
√𝟔𝟑
5. 6.
4
2
Pythagorean Theorem Exit Ticket Name:
Solve for x.
1) 2)
Pythagorean Theorem Exit Ticket Name:
Solve for x.
1) 2)

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Triangles: Properties, Attributes, and Congruence

Unit Plan Overview and Description

Common Core State Standards

Week 1 Monday Day 1 Tuesday Wednesday Day 2 Thursday Friday Day 3

Once students have practice on

After this real world Assessment:

Level Standard Lesson Duration: 90 minutes

Standard Alignment (state and national):

SUMMARY OF TEACHING TASKS/ACTIONS:

Estimated Time: Teacher Does: Students Do:

Classifying Triangles Slide Show

4. If the perimeter is 47, find x and the lengths

Holt McDougal Geometry

Holt McDougal Geometry

Holt McDougal Geometry

Recall that a triangle ( ) is a polygon

Holt McDougal Geometry

Holt McDougal Geometry

Triangle Classification By Angle Measures

Three acute angles

Holt McDougal Geometry

Triangle Classification By Angle Measures

Three congruent acute angles

Holt McDougal Geometry

Triangle Classification By Angle Measures

One right angle

Holt McDougal Geometry

Triangle Classification By Angle Measures

One obtuse angle

Holt McDougal Geometry

Triangle Classification By Side Lengths

Three congruent sides

Holt McDougal Geometry

Triangle Classification By Side Lengths

At least two congruent sides

Holt McDougal Geometry

Triangle Classification By Side Lengths

Holt McDougal Geometry

Classify FHG by its angle measures.

EHG is a right angle. Therefore mEHF +mFHG = 90°.

FHG is an equiangular triangle by definition.

Holt McDougal Geometry

Classify ACD by its side lengths.

From the figure, . So AC = 15, and ACD is

Holt McDougal Geometry

3. Find the side lengths of △ JKL.

Classify each triangle by its angles and sides.

4. Find the side lengths of the triangle.

5. Find the indicated angle measurement.

Level Standard Lesson Duration: 90 minutes

Standard Alignment (state and national):

SUMMARY OF TEACHING TASKS/ACTIONS:

Estimated Time: Teacher Does: Students Do:

Triangle Midsegment Theorem Warm Up

Distance Formula: √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2

1. Find X and Y, the midpoints of AC and CB.

2. Find the length of XY.

3. Find the length of AB.