1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

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

8. Theorem Right Triangle Congruence

9. 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

10. 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

11. 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

12. 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

13. Prove Right Triangle Congruence
Answer:
Example 2

14. 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

15. 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

16. Prove Right Triangle Congruence
Answer:
Example 2

17. 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

18. 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

19. Prove Right Triangles Congruent
Answer:
Example 3