This document contains examples and explanations of right triangles and proofs of triangle congruence using corresponding parts of right triangles or angle-side-angle (ASA) logic. It demonstrates that the legs of a right triangle are perpendicular and uses examples to prove triangles congruent when their corresponding parts are equal. One proof shows two right triangles are congruent because they share a right angle and two equal sides, applying the Hypotenuse-Leg theorem.

1. ACTIVITY 8

2. (
)

5. The legs are the two
shorter sides of a right
triangle.
The legs of a right triangle
are perpendicular to each
other.

7. EXAMPLE

8. *HY is congruent to
LE
*HP is congruent to
LG
*So, ΔHYP ≅ ΔLEG.

9. GIVEN:
PROVE:

10. PROOF:
STATEMENT REASON
MT ⊥ AH ?
AM≅MH ?
∠MTA and ∠MTH are right
angles
?
ΔMTA and
ΔMTH are right triangles.
?
MT ≅ MT ?
ΔMAT ≅ ΔMHT ?

11. GIVEN

16. HyL
Congruence
Theorem

21. * AC ≅ XZ
* ∠ 퐶 ≅ ∠ 푍
* So, Δ 퐴퐵퐶 ≅
Δ 푋푌푍

22. GIVEN:
PROVE:

23. STATEMENTS REASONS
∠ 퐴 ≅ ∠ 퐷 GIVEN
AB ≅ 퐷퐸 GIVEN
∠ 퐶 ≅ ∠ 퐹 DEFINITION OF RIGHT
ANGLES
Δ 퐴퐵퐶 ≅ Δ 퐷퐸퐹 ASA CONGRUENCE
Δ 퐴퐵퐶 ≅ Δ 퐷퐸퐹 HyA CONGRUENCE POSTULATE

24. :SUMMARIZATION: