Maths Grade 9 Term 2 Lesson Plans
Maths Grade 9 Term 2 Lesson Plans
Maths Grade 9 Term 2 Lesson Plans
DURATION: 1 Hour
By the end of the lesson learners should know and be able to:
revise properties and definitions of triangles in terms of their sides and angles, distinguishing
between:
- equilateral triangles.
- isosceles triangles.
- right-angled triangle.
types of triangles
properties of triangles
4. PRIOR KNOWLEDGE: constructions
Activity 1
Possible responses
Learners observed that each interior angle of the
triangle measures60 ° .
Learners observed that all sides of the triangle
are equal in length
Activity 3
Possible responses
B C
a) Emphasise that:
The sum of interior angles of a triangle is 1800.
An equilateral triangle has all sides equal and each interior angle = 600.
Isosceles triangle has at least two equal sides opposite the equal angles.
Right – angled triangle has one angle that is a right angle and the side opposite it
called hypotenuse which is always the longest side.
Homework
DURATION: 1 Hour
Note:Two triangles are congruent if they have exactly the same shape and size i.e. they are able
to fit exactly on top of each other. This means that all three corresponding sides and three
corresponding angles are equal, as shown in the following two pairs.
ΔABC ≡ ΔDEF and ΔGHI ≡ ΔJKL. In each pair, the corresponding sides and angles are equal.
Conditions Congruent
(Yes or No)
3 sides (SSS)
3 angles (AAA)
2 angles and a side (SAA)
2 sides (SS)
DBE workbook 1 Grade 9 page 140 – 141 No. 1 (e), No. 2 and 3
two angles and a side of the one triangle are equal to two corresponding angles
and a side of the other triangle. (AAS)
The corresponding sides of two triangles are the sides that are in the
same position relative to the angles of the triangles.
right-angle, hypotenuse and a side of one triangle are equal to the corresponding
right-angle, hypotenuse and a side of the other triangle (R,H,S)
Hypotenuse – The side opposite the right angle in a right-angled triangle
Carefully select appropriate activities from the Sasol-Inzalo Book 1, DBE workbooks
and/or textbooks for learners’ homework. The selected activities should address
different cognitive levels.
Homework: Sasol-Inzalo Book 1 Grade 9 page 208 – 209 no. 1-6
DURATION: 1 Hour
1.TOPIC: GEOMETRY OF 2D SHAPES: Similar and Congruent triangles (Lesson 3)
2.CONCEPTS & SKILLS TO BE ACHIEVED:
By the end of the lesson learners should know and be able to establish through investigation
the conditions for congruent triangles
Note:Two triangles are congruent if they have exactly the same shape and size i.e. they are able
to fit exactly on top of each other. This means that all three corresponding sides and three
corresponding angles are equal, as shown in the following two pairs.
ΔABC ≡ ΔDEF and ΔGHI ≡ ΔJKL. In each pair, the corresponding sides and angles are equal.
Conditions Congruent
(Yes or No)
3 sides (SSS)
3 angles (AAA)
2 angles and a side (SAA)
2 sides (SS)
DBE workbook 1 Grade 9 page 140 – 141 No. 1 (e), No. 2 and 3
The corresponding sides of two triangles are the sides that are in the
same position relative to the angles of the triangles.
right-angle, hypotenuse and a side of one triangle are equal to the corresponding
right-angle, hypotenuse and a side of the other triangle (R,H,S)
Hypotenuse – The side opposite the right angle in a right-angled triangle
Carefully select appropriate activities from the Sasol-Inzalo Book 1, DBE workbooks
and/or textbooks for learners’ homework. The selected activities should address
different cognitive levels.
Homework: Sasol-Inzalo Book 1 Grade 9 page 208 – 209 no. 1-6
DURATION: 1 Hour
Activity 2
The order in which we write the letters when stating that two triangles are congruent is very
important. The letters of the corresponding vertices between the two triangles must appear in the
same position in the notation. For example, the notation for the triangles above should be: ΔABC ≡
ΔXYZ, because it indicates that ^ A=^ ^ = ^Z , AB = XY, BC = YZ and AC = XZ.
X , ^B = Y^ , C
It is incorrect to write ΔABC ≡ ΔZYX. Although the letters refer to the same triangles, this notation
indicates that ^ A = ^Z , C
^=^X , AB = ZY and BC = YX, and these statements are not true.
Write down the equal angles and sides according to the following notations:
1. ΔKLM ≡ ΔPQR
2. ΔFGH ≡ ΔCST
Note:
Guard against the misconception that the use of the angles to notate the congruency might create
the impression that equal angles in triangles are a condition for congruency.
Work through the example with the learners showing them how to
use the four conditions of congruency for triangles to prove that
two triangles are congruent.
Example:
B
A
C
E copy example in their
notebooks.
Solution:
Statement Reason
1) AD = DC Given
2) A ^ ^E
DB = C D Vert. opp. ∠s
∴ ΔABD ≡ ΔCED
Note:
C B
X Z
W
9. CONSOLIDATION/CONCLUSION & HOMEWORK (Suggested time: 5 minutes)
a) Emphasise that:
to prove two triangles congruent, one of the four conditions for congruency must
be met.
use the correct notation for congruency.
always provide a reason for the conclusion.
Homework:
1. Prove that QR=SR. (Hint prove that the triangles are congruent)
Q R
*
* S
P
2. Prove that the triangles below are congruent. Then find the size of Q ^
M P.
MATHEMATICS LESSON PLAN GRADE 9
TERM 2: April - June
DURATION: 1 Hour
measuring of angles
4. PRIOR KNOWLEDGE: measuring of lines segments
ratio
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time: 10 minutes)
Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore, it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.
Ask learners to give their understanding of the concept similarity. Use various objects (e.g. leaves
from a tree,) to illustrate the meaning of similarity. Present learners with different objects and ask
them to identify similar figures.
Note:
Two triangles are similar if they have exactly the same shape but not necessarily the same size
i.e. the one is normally an enlargement of the other.
Note:
A D
B C
E F
Make sure that the triangles that are used in this activity are similar.
^B ^
D
measure angles
^
A ^
E
^
C ^
F
BA DE BA:DE =
measure the lengths
BC DF BC:DF = of the sides of
triangles
CA FE CA:FE =
Note:
When proving that triangles are similar, you either need to show that the:
a) Emphasise that:
two triangles are similar if corresponding angles are equal or the corresponding
sides are proportional (in the same ratio).
we use the symbol (///) to show similarity between triangles e.g. △ ABC /// △≝¿
Homework
1. Decide whether the following set of triangles are similar. Give reasons for your
decision.
(a)
18
36
(b)
(c)
G
C
9 cm
6 cm 13,5 cm
B 3 cm F
9 cm
A H 4,5 cm
E
By the end of the lesson learners should know and be able to solve geometric problems
involving unknown sides and angles in triangles and quadrilaterals, using known properties
of triangles and quadrilaterals, as well as properties of similar triangles.
3. RESOURCES: DBE workbook, Sasol-Inzalo Book 1, textbooks
Activity 2
D
*
# @
B C
# @
E F
The correct notation is very important when naming the similarity between triangles. For example, the
notation for the triangles above should be: Δ ABC /// Δ DEF, because it indicates that ^
A=^
D,
^B = ^ ^ =^ AB BC AC
E,C F and = =
DE EF DF
Activity 1
1. Study the figure below and answer the questions that follow.
Solution
Statement Reason
A ^BC = P QC
^ common
B^
AP =Q^
PC Corresponding ∠s (AB // PQ)
AB BC AC
= = Δ ABC /// Δ PQC
PQ QC PC
follow demonstration and
engage in questions as
demonstration unfolds.
AB 10
=
2 4
4 AB=20
AB=5 units
Activity 2
P S
B
Possible solution
AB BC AC
= = (Given ∆ ABC /// ∆ PTS)
PT TS PS
6 12
= Substitute the given sides
2 x
6 12 Cross multiply
=
2 x
6 x=24
Applying the
6 x 24 multiplicative inverse
=
6 6
x=4 cm
P Q
72 mm
56 mm 42 mm
R 70 mm S
R S
2. Consider the similar triangles drawn below using concentric circles. Explain why the
triangles are similar in each diagram.
I H
J K Y
M
F
Figure 1 Figure 2
MATHEMATICS LESSON PLAN GRADE 9
TERM 2: April - June
DURATION: 1 Hour
By the end of the lesson learners should know and be able to, solve geometric
problems involving unknown sides and angles in triangles and quadrilaterals, using known
properties of triangles and quadrilaterals, as well as properties of congruent and similar
triangles.
Homework provides an opportunity for teachers to track learner’s progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.
Activity 1
D C
A C
E
D
Activity 1
Activity 2
KMNO is a parallelogram. Study the diagram below and calculate the values of x∧ y
120 °
DURATION: 1 Hour
By the end of the lesson learners should know and be able to solve geometric
problems involving unknown sides and angles in triangles and quadrilaterals, using
known properties of triangles and quadrilaterals, as well as properties of congruent and
similar triangles.
Homework provides an opportunity for teachers to track learner’s progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.
6. INTRODUCTION (Suggested time: 5 Minutes)
Give learners a few simple equations to solve for unknowns such as:
a) 4 x+5 x=180 °
b) a+ 30° =90 °
Activity 1
76°
2 44°
N S
(Expected answer)
(Interior angles of triangle) complete the activities
given by the teacher.
NB: give learners the opportunity to verify their solutions by
substituting the value of x into the original equation.
Activity 2
Let learners calculate the value of y with reasons:
y 45o
D^
EF + D ^
FE + E^
D F = 180o (sum angles of a triangle)
^ F=180 °
45 ° + 45°+ E D
E^
D F=180 ° – 90 °
E^ D F=90 °
^ F
y= D+ ^ (exterior angle of a ∆ = sum of 2 opp. Int. angles)
y=45 °+ 90 °
y=135 °
Homework
Activity
In the figure below KM ∨¿ NP, ln=LP and N ^L P=120° . Determine, with reasons,
^M
the size of T L
T
K L M
N P