Sas 1
Sas 1
Sas 1
School
Teacher Rosemarie T. Bernal Learning Area MATHEMATICS
Teaching Dates MARCH 21, 2023 Quarter Third Quarter
DETAILED LESSON and Time 7:45-8:45 am and 1:00-
PLAN 2:00 pm
Quarter 3, Week 6
I. OBJECTIVES
The learner demonstrates understanding of key concepts of axiomatic structure of
A. Content standards
geometry and triangle congruence
The learner is able to
a. Formulate an organized plan to handle a real-life situation
b. Communicate mathematical thinking with coherence and clarity in
B. Performance Standards
formulating, investigating, analyzing, and solving real-life problems
involving congruent triangles using appropriate and accurate
representations.
Most Essential Learning Competency: The learner proves two triangles are
congruent (M8GE-IIIg-1)
C. Learning Competencies / At the end of the discussion the learner should be able to:
Objectives a. Use SAS triangle congruence postulates and theorems to prove that two
triangles are congruent
b. Use the two-column proof in proving two triangles are congruent
The SAS If AB ≅ DE ,
Congruence ∠ B ≅ ∠ E ,∧BC ≅ EF , then ∆ ABC
Postulate
Directions: Fill in the missing statements and reasons in the two-column proof
below. Answer the questions that follow.
C A
Given: ∎ CARE is a square and CR is its diagonal
Prove: ∆ CER ≅ ∆ CAR
E R
Proof:
Statements Reasons
1. ___________________ Given
2. ___________________ Definition of Square
3. ___________________ Reflexive Property of Congruence
4. ∆ CER ≅ ∆ CAR _____________________________
Now that you have already an in depth understanding regarding Triangle
Congruence Postulate, let us now proceed with our new lesson, proving two
congruent triangles.
DRILL
Activity: You be the Judge! Decide whether enough information is given to show
that the triangles are congruent. If so, tell which congruence postulate you would
use.
SIDE-SIDE-SIDE ANGLE-ANGLE-SIDE
Congruence Postulate Congruence Postulate
SIDE-ANGLE-SIDE ANGLE-SIDE-ANGLE
Congruence Postulate Congruence Postulate
Solution:
a. From the diagram, we that AB ≅ CB∧DB ≅ DB .
The angle included between AB∧DB is ∠ ABD
The angle included between CB∧DB is ∠CBD
Because the included angles are congruent, we can use the SAS
Congruence Postulate to conclude that ∆ ABD ≅ ∆ CBD .
b. We know that GF ≅ GH ∧¿ ≅ ¿. However, the congruent angles are not
included between the congruent sides, so we cannot use the SAS
Congruence Postulate.
D. Discussing New Concepts
and Practicing New Skills In this lesson we are going to use SAS congruence postulate in proving two
congruent triangles.
Identify what the given are, and what is to be proved. Marked the given
information on the diagram.
Identify the congruence theorem to be used and the additional information
and why
Write down the statements and the reason in a two-column proof. Make
the last statement contains what should be proved.
Now, let us apply the congruence postulates and theorems in proving congruent
triangles using the illustrative examples below.
Example 1: Q
P
R S
Step 2: Identify the congruence theorem to be used and the additional information
and why.
QP bisects ∠ RQS , QP is the angle bisector , so the angle ∠RQP ≅ ∠ SQP are
congruent by Definition of Angle Bisector. Then, QP is the common side of
∆ RQP∧∆ SQP , so by reflexive property of congruence , hence SAS
congruence postulate can be used to prove ∆ RQP ≅ ∆ SQP
Step 3: Write down the statements and the reason in a two-column proof. Make
the last statement contains what should be proved.
Two-column proof:
Statements Reasons
1. QR ≅ QS Given
2. QP bisects ∠ RQS Given
3. ∠ RQP ≅ ∠ SQP Definition of angle bisector
4. QP ≅ Q P Reflexive Property of Congruence
5. ∆ RQP ≅ ∆ SQP SAS Congruence Postulate
We were able to show the congruence of the two triangles using SAS congruence
postulate.
Proof: C
Statements Reasons
1. AD bisects ∠ CAB Given
2. AC ≅ AB Given
3. ∠ CAD ≅ ∠ BAD Definition of Angle Bisector
4. AD ≅ AD Reflexive Property of Congruence
5. ∆ CAD ≅ ∆ BAD SAS Congruence Postulate
We were able to show the congruence of the two triangles using SAS congruence
postulate.
E. Developing Mastery R
Try this!
A U
N
Take a look at the figure. Given that RA ≅ RU , RN bisects ∠ ARU . Prove
∆ ARN ≅ ∆ URN . Use the two-column proof to prove the triangle congruence.
Proof:
Statements Reasons
1. RA ≅ RU Given
2. RN bisects ∠ ARU Given
3. ∠ ARN ≅ ∠URN Definition of angle bisector
4. RN ≅ RN Reflexive Property of Congruence
5. ∆ ARN ≅ ∆ URN SAS Congruence Postulate
How do you find the activity? Did you find it difficult to prove the congruence of
two triangles?
Direction:
Prove that two triangles are congruent by completing the two-column proof.
Provide all the necessary reasons.
P
M N
Given: OM ≅ ON
OP bisects ∠ MON
Prove: ∆ MOP ≅ ∆ NOP
O
I. Additional Activities for List down at least five things in your house, buildings or other structures found in
your community where congruent triangles are used. Explain the importance of
Application or Remediation
congruent triangles in these structures.
V. REMARKS
VI. REFLECTION
No. of learners who earned 80%
in the evaluation