1. Proving Triangles Congruent – ASA, AAS
LESSON 4–5
Proving Triangles Congruent – ASA, AAS

2. Five-Minute Check (over Lesson 4–4) TEKS 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
Proof: Angle-Angle-Side Theorem
Example 2: Use AAS to Prove Triangles Congruent
Example 3: Real-World Example: Apply Triangle Congruence
Concept Summary: Proving Triangles Congruent
Lesson Menu

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

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

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

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

7. 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

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

9. Mathematical Processes G.1(B), Also addresses G.1(G)
Targeted TEKS
G.6(B) Prove two triangles are congruent by applying
the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side,
Angle-Angle-Side, and Hypotenuse-Leg congruence conditions.
G.6(D) Verify theorems about the relationships in
triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, mid-segments, and medians, and apply these relationships to
solve problems. Also addresses G.5(C).
Mathematical Processes
G.1(B), Also addresses G.1(G)
TEKS

10. 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

11. included side
Vocabulary

12. Concept

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

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

15. Fill in the blank in the following paragraph proof.
A. SSS B. SAS
C. ASA D. AAS
Example 1

16. Theorem

17. Proof

18. Write a paragraph proof.
Use AAS to Prove Triangles Congruent
Write a paragraph proof.
Proof: NKL  NJM, KL  MN, and N  N by the Reflexive property. Therefore, ΔJNM  ΔKNL by AAS. By CPCTC, LN  MN. __
___
Example 2

19. Complete the following flow proof.
A. SSS B. SAS
C. ASA D. AAS
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 cm and the height of the isosceles triangle is 3 cm, find PO.
Example 3

21. NV  EN by definition of isosceles triangle
Apply Triangle Congruence
In order to determine the length of PO, we must first prove that the two triangles are congruent.
____
ΔENV  ΔPOL by ASA.
NV  EN by definition of isosceles triangle
____
EN  PO by CPCTC.
____
NV  PO by the Transitive Property of Congruence.
____
Since the height is 3 centimeters, we can use the Pythagorean theorem to calculate PO. The altitude of the triangle connects to the midpoint of the base, so each half is 4. Therefore, the measure of PO is 5 centimeters.
Answer: PO = 5 cm
Example 3

22. The curtain decorating the window forms 2 triangles at the top
The curtain decorating the window forms 2 triangles at the top. B is the midpoint of AC. AE = 13 inches and CD = 13 inches. BE and BD each use the same amount of material, 17 inches. Which method would you use to prove ΔABE  ΔCBD?
A. SSS
B. SAS
C. ASA
D. AAS
Example 3

23. Concept

24. Proving Triangles Congruent – ASA, AAS
LESSON 4–5
Proving Triangles Congruent – ASA, AAS