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Hypotenuse Leg Congruence Theorem Extension

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Presentation on theme: "Hypotenuse Leg Congruence Theorem Extension"— Presentation transcript:

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


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