1. Splash Screen

2. Concept

3. Write a two-column proof.
Use ASA to Prove Triangles Congruent
Write a two-column proof.
Example 1

4. 4. Alternate Interior Angles
Use ASA to Prove Triangles Congruent
Proof:
Statements Reasons
1. Given
1. L is the midpoint of WE.
____ 2.
2. Midpoint Theorem 3.
3. Given
4. W  E
4. Alternate Interior Angles
5. WLR  ELD
5. Vertical Angles Theorem
6. ΔWRL  ΔEDL
6. ASA
Example 1

5. Concept

6. Write a paragraph proof.
Use AAS to Prove Triangles Congruent
Write a paragraph proof.
Example 2

7. 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 cm and the height of the isosceles triangle is 3 cm, find PO.
Example 3

8. Concept

9. Proving RIGHT TRIANGLES congruent
*As long as statement(s) mention right angles,
you only need 2 congruent pieces in each triangle: each hypotenuse
and corresponding legs. Hence, HL.
Concept

10. Example 4: Determine whether each pair of triangles is congruent.
If yes, state the postulate/theorem that applies.
Each triangle has right angles that are congruent, a 2nd set of corresponding angles that are congruent, and a side in between the 2 angles that is congruent.
ASA
Each triangle has right angles that are congruent, a 2nd set of corresponding angles that are congruent, and a 3rd set of corresponding angles that are congruent.
NOT POSSIBLE.
(AAA does not exist)
Each triangle has right angles that are congruent, a set of corresponding sides that are congruent, and share a side, but SSA does not exist. (the angle is not the included angle). However, because the triangles are right triangles, they share the hypotenuse, and have a set of congruent legs. HL
Concept

11. Given: AB  BC, DC  BC, AC  BD
Example 5: Complete the proof.
Given: AB  BC, DC  BC, AC  BD
Prove: ΔABC ΔDCB
Proof:
Reasons
Statements 1. 2.
3. Given
4. Definition of  5.
6. Reflexive Property 7.
Given
Definition of 
DCB is a right angle
Given HL
ΔABC ΔDCB
Concept

12. End of the Lesson

13. Five-Minute Check (over Lesson 4–4) CCSS 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
Concept Summary: Proving Triangles Congruent
Lesson Menu

14. 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. ASA
C. SAS
D. not possible
5-Minute Check 1

15. 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. ASA
C. SAS
D. not possible
5-Minute Check 2

16. 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. SAS
B. AAS
C. SSS
D. not possible
5-Minute Check 3

17. 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. SSA
B. ASA
C. SSS
D. not possible
5-Minute Check 4

18. 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. AAA
B. SAS
C. SSS
D. not possible
5-Minute Check 5

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

20. G.CO.10 Prove theorems about triangles.
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.
Mathematical Practices
3 Construct viable arguments and critique the reasoning of others.
5 Use appropriate tools strategically.
CCSS

21. You proved triangles congruent using SSS and SAS.
Use the ASA Postulate to test for congruence.
Use the AAS Theorem to test for congruence.
Then/Now

22. included side
Vocabulary