1. Five-Minute Check (over Lesson 4–3) Mathematical Practices Then/Now
New Vocabulary
Postulate 4.3: Angle-Side-Angle (ASA) Congruence
Example 1: Use ASA to Prove Triangles Congruent
Theorem 4.5: Angle-Angle-Side (AAS) Congruence
Example 2: Use AAS to Prove Triangles Congruent
Example 3: Real-World Example: Apply Triangle Congruence
Lesson Menu

2. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.
A. SSS
B. SAS
C. not possible
5-Minute Check 1

3. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.
A. SSS
B. SAS
C. not possible
5-Minute Check 2

4. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.
A. SSS
B. SAS
C. not possible
5-Minute Check 3

5. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.
A. SSS
B. SAS
C. not possible
5-Minute Check 4

6. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.
A. SSS
B. SAS
C. not possible
5-Minute Check 5

7. Given A  R, what sides must you know to be congruent to prove ΔABC  ΔRST by SAS?
5-Minute Check 6

8. Mathematical Practices
3 Construct viable arguments and critique the reasoning of others.
Content Standards
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. MP

9. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. MP

10. You proved triangles congruent using SSS and SAS.
Use the ASA congruence criterion to prove triangles congruent.
Use the AAS congruence criterion to prove triangles congruent.
Then/Now

11. included side
New Vocabulary

12. Postulate

13. Write a two-column proof. Given:
Use ASA to Prove Triangles Congruent
Write a two-column proof.
Given:
Prove: WRL ≅ EDL
Example 1

14. Use ASA to Prove Triangles Congruent
WR ǁ ED, L is the midpoint of WE Write the given statements.
Why is WL ≅ LE? The Midpoint Theorem.
Why is  W ≅  E? Alternate Interior Angles Theorem.
Why is  WLR ≅  ELD? Vertical Angles Theorem.
Why is ∆WRL ≅ ∆EDL? ASA
Use the information to write a two-column proof.
Example 1

15. Use ASA to Prove Triangles Congruent
Answer:
Example 1

16. Theorem

17. Write a paragraph proof. Given: NKL ≅ NJM
Use AAS to Prove Triangles Congruent
Write a paragraph proof.
Given: NKL ≅ NJM
Prove:
Example 2

18. Use AAS to Prove Triangles Congruent
KL ≅ JM,  NKL ≅  NJM Write the given statements.
Why is  N ≅  N? The Reflexive Property.
Why is ∆ JNM ≅ ∆ KNL? AAS
Why is LN ≅ MN CPCTC
Use the information to write a paragraph proof.
Example 2

19. Use AAS to Prove Triangles Congruent
Answer:
Example 2

20. Apply Triangle Congruence
MANUFACTURING Barbara designs a paper template for a certain envelope. She designs the top and bottom flaps to be isosceles triangles that have congruent bases and base angles. If EV = 8 centimeters and the height of the isosceles triangle is 3 centimeters, find PO.
Real-World Example 3

21. Answer: PO = 5 cm Apply Triangle Congruence
EV≅ PL , The height of ∆ POL = 3 and is the midpoint of PL Write the given statements. 1 2
PL = The Midpoint Theorem.
= (PO) Use the Pythagorean Theorem to find PO.
PO = 5
Answer: PO = 5 cm
Real-World Example 3