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Objective: The students will be able to Prove Right Triangle Congruence – LL, HA, LA and HL.

Prove Right Triangle Congruence LL, HA, LA and HL. Chapter 4 – Lesson 5 Prove Right Triangle Congruence LL, HA, LA and HL.

Theorem 4.6 (LL) (leg-leg congruence) If the legs of one right triangle are congruent to the legs of another right triangle, then the triangles are congruent.

Are the triangles congruent? Yes Name the theorem or postulate that applies? LL What rigid motions map the top triangle onto the bottom one? A 90⁰ counterclockwise rotation and a horizontal reflection.

Theorem 4.7 (HA) (hypotenuse-angle congruence) If the hypotenuse and acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle then the two triangles are congruent.

Are the triangles congruent? Yes Name the theorem or postulate that applies? HA What rigid motions map the top triangle onto the bottom one? A 180⁰ clockwise rotation.

Theorem 4.8 (LA) (leg-angle congruence) If the one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent

Are the triangles congruent? Yes Name the theorem or postulate that applies? LA What rigid motions map the top triangle onto the bottom one? A horizontal reflection followed by a 90⁰ counterclockwise rotation and a translation.

Theorem 4.9 (HL) (hypotenuse-leg congruence) If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of a second right triangle then the triangles are congruent

FEG and HIG are right s. Given: FEG and HIG are right s. Prove: FEG HIG G Proof: E H 1. Given 1. Reasons Statements 2. Given 2. 3. 3. Midpoint Theorem 4. FEG and HIG are right s. 4. Given 5. FEG HIG 5. HL Example 4-1b

ACD and ACB are right s. Given: Prove: ABC ADC ACD and ACB are right s. Proof: Statements Reasons 1. ACD and ACB are right s. 1. Given 2. 2. Given 3. 3. Reflexive 4. 4. HL ABC ADC Example 4-3c

That the triangles are right triangles.

Kahoot!

Lesson Summary: Objective: The students will be able to Prove Right Triangle Congruence – LL, HA, LA and HL.

Preview of the Next Lesson: Objective: The students will be able to write proofs using Theorems and Corollaries of Isosceles and Equilateral Triangles and solve problems involving Isosceles and Equilateral Triangles.

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