1. Lesson 4-4 & 4.5: Proving Δs Congruent
TARGETS
Use the SSS, SAS, ASA, AAS Postulates to test for triangle congruence.
Target

2. Side-Side-Side (SSS) Congruence
LESSON 4-4 & 4-5: Proving Triangles Congruent
Side-Side-Side (SSS) Congruence
3 pairs of corresponding sides are congruent
SSS Congruence

3. 2 pairs of corresponding sides and their included
LESSON 4-4 & 4-5: Proving Triangles Congruent
Side-Angle-Side (SAS) Congruence
2 pairs of corresponding sides and their included
angles are congruent
SAS Congruence

4. 2 pairs of corresponding angles and their included
LESSON 4-4 & 4-5: Proving Triangles Congruent
Angle-Side-Angle (ASA) Congruence
2 pairs of corresponding angles and their included
sides are congruent
ASA Congruence

5. Angle-Angle-Side (AAS) Congruence
LESSON 4-4 & 4-5: Proving Triangles Congruent
Angle-Angle-Side (AAS) Congruence
2 pairs of corresponding angles and their
non-included sides are congruent
AAS Congruence

6. Which Method? SSS AAS ASA SAS
LESSON 4-4 & 4-5: Proving Triangles Congruent
Which Method?
SSS
AAS
ASA
SAS
Which Method?

7. LESSON 4-4: SSS, SAS Congruence
EXAMPLE 2
EXTENDED RESPONSE Triangle DVW has vertices D(–5, –1), V(–1, –2), and W(–7, –4). Triangle LPM has vertices L(1, –5), P(2, –1), and M(4, –7). a. Graph both triangles on the same coordinate plane. b. Use your graph to make a conjecture as to whether the triangles are congruent. Explain your reasoning. c. Write a logical argument that uses coordinate geometry to support the conjecture you made in part b.
Example 2A

8. Read the Test Item You are asked to do three things in this problem
Read the Test Item You are asked to do three things in this problem. In part a, you are to graph ΔDVW and ΔLPM on the same coordinate plane. In part b, you should make a conjecture that ΔDVW  ΔLPM or ΔDVW  ΔLPM based on your graph. Finally, in part c, you are asked to prove your conjecture. /
Solve the Test Item a.
Example 2B

9. b. From the graph, it appears that the triangles have the same shapes, so we conjecture that they are congruent.
c. Use the Distance Formula to show all corresponding sides have the same measure.
Example 2C

10. Example 2C

11. Answer:. WD = ML, DV = LP, and VW = PM
Answer: WD = ML, DV = LP, and VW = PM. By definition of congruent segments, all corresponding segments are congruent. Therefore, ΔWDV  ΔMLP by SSS.
Example 2 ANS

12. Determine whether ΔABC  ΔDEF for A(–5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1).
A. yes
B. no
C. cannot be determined A B C
Example 2A