This PowerPoint presentation is all about proving triangle congruence. This was utilized during the synchronous lecture with Grade 8 students. This contains all of the elements of a lesson plan, which includes lecture notes, activities, and practice exercises.
6. LEARNING COMPETENCY
At the end of our lesson, you will be able to:
• prove that two triangles are congruent.
(M8GE-IIIg-1)
7. WORD BANK
SSS Congruence Postulate
SAS Congruence Postulate
ASA Congruence Postulate
Reflexive Property
Symmetric Property
Transitive Property
LET'S RECALL
8. LET'S RECALL
If the two sides and an included
angle of one triangle are
congruent to the corresponding
two sides and the included angle
of another triangle, then the
triangles are congruent. What
congruence postulate I am?
SAS Congruence Postulate
9. LET'S RECALL
If the two angles and the
included side of one triangle are
congruent to the corresponding
two angles and an included side
of another triangle, then the
triangles are congruent. What
congruence postulate I am?
ASA Congruence Postulate
10. LET'S RECALL
If the three sides of one triangle
are congruent to the three sides
of another triangle, then the
triangles are congruent. What
congruence postulate I am?
SSS Congruence Postulate
15. STEPS IN PROVING TRIANGLE CONGRUENCE
1. Label your diagram with all the given information.
A
B
C
F D
E
Given:
Prove:
16. STEPS IN PROVING TRIANGLE CONGRUENCE
2. Analyze your diagram to see what else you can find that
is congruent.
3. Decide what method you are going to use to prove that
the triangles are congruent.
17. STATEMENTS REASONS
1. 1.
2. 2.
3. 3.
4. 4.
TWO-COLUMN PROOF
Proofs
If-then statements
Conclusions
Statements
“why we know what we know?”
18. STEPS IN PROVING TRIANGLE CONGRUENCE
4. Start your proof. List your given information and state
“Given” as your reason.
STATEMENTS REASONS
1. 1.
2. 2.
3. 3.
4. 4.
Given
Given
Given
19. STEPS IN PROVING TRIANGLE CONGRUENCE
5. Continue to enumerate your statements together with
their proofs on the opposite column.
STATEMENTS REASONS
1. 1.
2. 2.
3. 3.
4. 4.
Given
Given
Given
20. STEPS IN PROVING TRIANGLE CONGRUENCE
6. Lastly, show your triangles are congruent using a
congruence statement and a reason.
STATEMENTS REASONS
1. 1.
2. 2.
3. 3.
4. 4.
Given
Given
Given
SSS Congruence Postulate
21. STEPS IN PROVING TRIANGLE CONGRUENCE
1. Label your diagram with all the given information.
2. Analyze your diagram to see what else you can find that is congruent.
3. Decide what method you are going to use to prove that the triangles
are congruent.
4. Start your proof. List your given information and state “Given” as your
reason.
5. Continue to enumerate your statements together with their proofs on
the opposite column.
6. Lastly, show your triangles are congruent using a congruence statement
and a reason.
22. EXAMPLE # 1
C A
R
E
STATEMENTS REASONS
1. Square CARE, 𝐶𝑅
is a diagonal.
1. Given.
2. 𝐶𝐸 ≅ 𝐴𝑅,
𝐶𝐴 ≅ 𝐸𝑅
2. __________________
3. ________________ 3. Reflexive Property
4. ∆𝐶𝐸𝑅 ≅ ∆𝐶𝐴𝑅 4. __________________
Definition of a square
SSS Congruence Postulate
23. EXAMPLE # 2
Given:
Prove:
STATEMENTS REASONS
1. ∠𝐸𝑇𝑃 ≅ ∠𝐴𝑇𝑃
∠𝐸𝑃𝑇 ≅ ∠𝐴𝑃𝑇
1.
2. 𝑃𝑇 ≅ 𝑃𝑇 2.
3. ∆𝑃𝐸𝑇 ≅ ∆𝑃𝐴𝑇
3.
Given
Reflexive Property
ASA Congruence
Postulate
E
P
A
T
24. EXAMPLE # 3
P
R
A
Y
STATEMENTS REASONS
1. Rhombus PRAY
and its diagonal 𝑅𝑌
1. _____________
2. 𝑃𝑅 ≅ 𝐴𝑅
𝑃𝑌 ≅ 𝐴𝑌
2. Definition of a
rhombus
3. _____________
3. Reflexive Property of
Congruence
4. _____________ 4. ______________
Given
SSS Congruence
Postulate
25. CONGRUENT TRIANGLES IN REAL-LIFE
TRUSS BRIDGE
Truss Railroad Bridge, San Jacinto
River, Crosby, Texas
Source: https://www.flickr.com/photos/nakrnsm/7917810766/
26. CONGRUENT TRIANGLES IN REAL-LIFE
STRUCTURES
WITH
TRIANGLES
by Designer Squad
Source: https://www.youtube.com/watch?v=mBHJtWbsiaA
