1. Hypotenuse Leg Congruence Theorem Extension

2. a and b are the legs of the right triangle a
Legs of a Right Triangle
Hypotenuse of a Right Triangle
Hypotenuse-Leg (HL) Congruence Theorem
 Any two right triangles with a congruent hypotenuse and a corresponding congruent leg are congruent triangles c
a and b are the legs of the right triangle a b c
c is the hypotenuse of a right triangle a b

3. Explain why these two triangles are congruent using the hypotenuse leg congruence theorem.
Corresponding leg = 𝐵𝐶 ≅ 𝐵𝐶
The hypotenuse of each triangle are congruent and each triangle has a corresponding side that is congruent so therefore they are congruent by HL.

4. Example 3:
Using the given postulate, tell which parts of the pair of triangles should be shown congruent.
𝑅𝑃 ≅ 𝑄𝑆

5. Try the you try before looking at the answer!

6. You Try! 1. Why can these two triangles be considered congruent?
The hypotenuse and legs are congruent, therefore the two triangles are congruent.

7. You Try! 2. Is it possible to show that JGH  HJK?
Yes, due to the reflexive property the hypotenuse 𝐽𝐻 ≅ 𝐽𝐻 , each triangle also has a corresponding leg that is congruent ( 𝐽𝐺 ≅ 𝐻𝐾 ).

8. Example 4: 𝐷𝐸 ⊥ 𝐹𝐶 ∠𝐷𝐸𝐹 & ∠𝐷𝐸𝐶 are right angles
𝐷𝐸 ⊥ 𝐹𝐶
∠𝐷𝐸𝐹 & ∠𝐷𝐸𝐶 are right angles
Definition of right angles
Given
𝐷𝐸 ≅ 𝐷𝐸
Reflexive Property
∆𝐷𝐸𝐹≅∆𝐷𝐸𝐶 HL

9. Example 5: 𝑃𝑄 ⊥ 𝑆𝑄 Definition of perpendicular
𝑃𝑄 ⊥ 𝑆𝑄
Definition of perpendicular
∆𝑃𝑅𝑆 & ∆𝑃𝑅𝑄 are right triangles
Given
𝑃𝑅 ≅ 𝑃𝑅
Reflexive Property
∆𝑃𝑅𝑄 ≅∆𝑃𝑅𝑆 HL

10. Try the you try before looking at the answer!

11. You Try! 𝑊𝑌 ≅ 𝑋𝑍 𝑊𝑍 ⊥ 𝑍𝑌 𝑋𝑌 ⊥ 𝑍𝑌 Definition of perpendicular
𝑊𝑍 ⊥ 𝑍𝑌
𝑋𝑌 ⊥ 𝑍𝑌
Definition of perpendicular
Definition of right angles
𝑍𝑌 ≅ 𝑍𝑌
∆WYZ ≅ ∆XZY HL