Five-Minute Check (over Lesson 4–4) Mathematical Practices Then/Now Theorem Right Triangle Congruence Example 1: Right Triangle Congruence Example 2: Prove Right Triangle Congruence Example 3: Real-World Example: Prove Right Triangles Congruent Lesson Menu

Refer to the figure. Complete the congruence statement Refer to the figure. Complete the congruence statement. ΔWXY  Δ_____ by ASA. ? A. ΔVXY B. ΔVZY C. ΔWYX D. ΔZYW 5-Minute Check 1

Refer to the figure. Complete the congruence statement Refer to the figure. Complete the congruence statement. ΔWYZ  Δ_____ by AAS. ? A. ΔVYX B. ΔZYW C. ΔZYV D. ΔWYZ 5-Minute Check 2

Refer to the figure. Complete the congruence statement Refer to the figure. Complete the congruence statement. ΔVWZ  Δ_____ by SSS. ? A. ΔWXZ B. ΔVWX C. ΔWVX D. ΔYVX 5-Minute Check 3

What congruence statement is needed to use AAS to prove ΔCAT  ΔDOG? A. C  D B. A  O C. A  G D. T  G 5-Minute Check 4

Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. Content Standards G.CO.10 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. MP

You proved triangles congruent using SSS, SAS, ASA, and AAS. Use the right triangle congruence theorems to prove relationships in geometric figures. Then/Now

Theorem Right Triangle Congruence

Right Triangle Congruence Determine whether the each pair of triangles is congruent. If yes, include the theorem or postulate that applies and describe the series of rigid motions that maps one triangle onto the other. Example 1

Answer: yes; LL; translation Right Triangle Congruence Are the two triangles congruent? Yes What theorem proves the triangles are congruent? LL What type of motion will map one triangle onto the other? Translation Answer: yes; LL; translation Example 1

Write the specified type of proof. Prove Right Triangle Congruence Write the specified type of proof. A. Flow proof Given: EFG and GHE are right triangles with right angles  F and  H; . Prove: EFG ≅ GHE Example 2

Prove Right Triangle Congruence ∆ EFG ≅ ∆ GHE are right triangles with right angles  F and  H Write the given statements. EF ǁ HG Write the given statements. Why is  FEG ≅  HGE? EF ǁ HG and alternate interior angles are congruent. Why is EG ≅ EG ? The Reflexive Property. Why is ∆ EFG ≅ ∆ GHE? HA Use the information to write a flow proof. Example 2

Prove Right Triangle Congruence Answer: Example 2

Write the specified type of proof. Prove Right Triangle Congruence Write the specified type of proof. B. Two-column proof Given: Prove: JKL ≅ MLK Example 2

Prove Right Triangle Congruence JL II KM ,  JKL and  MLK are right angles Write the given statements. Why is  MKL ≅  JLK? JL II KM and alternate interior angles are congruent. Why is KL ≅ KL ? The Reflexive Property. Why is ∆ JKL ≅ ∆ MLK? LA Use the information to write a two-column proof. Example 2

Prove Right Triangle Congruence Answer: Example 2

Given: RQ is a perpendicular bisector of PS. Prove: PQR ≅ SQR Prove Right Triangles Congruent Windows in a house form adjacent right triangles. Write a paragraph proof to prove that PQR ≅ SQR. Given: RQ is a perpendicular bisector of PS. Prove: PQR ≅ SQR Example 3

Prove Right Triangles Congruent RQ is a perpendicular bisector of PS Write the given statements. Why is  PQR and  SQR right angles? Definition of perpendicular. Why is RQ ≅ SQ ? Definition of bisector. Why is RQ ≅ RQ ? The Reflexive Property. Why is ∆ PQR ≅ ∆ SQR? LL Use the information to write a paragraph proof. Example 3

Prove Right Triangles Congruent Answer: Example 3