Triangle Congruence : Proving Statements

1. MATHEMATICS – 8
LIMITED FACE TO FACE CLASS
LARRY B. AZARIAS
Math Teacher -III

5. OBJECTIVES :
At the end of the lesson, the learners are expected to :
1. prove statements on congruent triangles;
2. determine the definitions, theorems and postulates that can
be used in proving triangle congruence;
3. participate actively in class discussion.

6. TRIANGLE
CONGRUENCE:
PROVING STATEMENTS

7. Definitions, Theorems, and Postulates that
can be used in Proving Triangle
Congruence
1. CPCTC
2. VERTICAL ANGLES THEOREM
3. PROPERTIES OF TRIANGLE CONGRUENCE
a. Reflexive Property of Triangle Congruence
b. Symmetric Property of Triangle Congruence
c.Transitive Property of Triangle Congruence
4. MEDIAN OF A TRIANGLE
5. EQUILATERAL TRIANGLE
6. LINE SEGMENT BISECTOR

8. CPCTC
CORRESPONDING
PARTS of
CONGRUENT
TRIANGLES are
CONGRUENT

9. VERTICAL ANGLES
THEOREM
If two angles are vertical angles,
then they are congruent.
Abbreviation
Vert. are

10. Example:
1
2
3
4
L1 L3 and L2 L4

11. PROPERTIES OF RIGHT TRIANGLE

14. Examples
1. Given: ΔAMR and ΔBGT are right triangles. LR ≅ LT, 𝑀𝑅 ≅ 𝐺𝑇
Prove: 𝐴𝑅 ≅ 𝐵𝑇

16. 2. Given: 𝐹𝐽 bisects L CJH, 𝐽𝐶 ≅ 𝐽𝐻
Prove: L C ≅ L H

18. ACTIVITY 1
Complete the proof :
Given: ΔBAC is an equilateral Δ. 𝐴𝑇 bisects 𝐵𝐶.
Prove: L BAT ≅ L CAT

20. APPLICATION:
Supply the necessary statement and reasons.
Given: ΔOPR is isosceles. 𝑃𝑆. is the median to the base 𝑂𝑅.
Prove: L O ≅ L R

22. EVALUATION :
Complete the proof
A. Given: 𝐸𝑀 and 𝐾𝑇 bisect each other at O.
Prove: M ≅ E

23. EVALUATION :

24. EVALUATION :
B. Given: 𝐴𝐶 bisects L BAD and L BCD
Prove: 𝐵𝐶 ≅ 𝐷𝐶

25. EVALUATION :

26. REFLECTION :
I understand that _____________________________________________.
I realized that_________________________________________________.
I need to learn more about____________________________________.