1. Concept 1

2. Write a flow proof. ___ Given: QU  AD, QD  AU Prove: ΔQUD  ΔADU
Use SSS to Prove Triangles Congruent
Write a flow proof.
Given: QU  AD, QD  AU
___
Prove: ΔQUD  ΔADU
Example 1

3. Use SSS to Prove Triangles Congruent
Answer: Flow Proof:
Example 1

4. Which information is missing from the flowproof. Given:. AC  AB
Which information is missing from the flowproof? Given: AC  AB D is the midpoint of BC. Prove: ΔADC  ΔADB
___
A. AC  AC
B. AB  AB
C. AD  AD
D. CB  BC
___ A B C D
Example 1 CYP

5. 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

6. 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).
Example 2B

7. 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).
Example 2C

8. 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).
Example 2C

9. 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

10. 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

11. Concept 2

12. Use SAS to Prove Triangles are Congruent
ENTOMOLOGY The wings of one type of moth form two triangles. Write a two-column proof to prove that ΔFEG  ΔHIG if EI  HF, and G is the midpoint of both EI and HF.
Example 3

13. Given: EI  HF; G is the midpoint of both EI and HF.
Use SAS to Prove Triangles are Congruent
Given: EI  HF; G is the midpoint of both EI and HF.
Prove: ΔFEG  ΔHIG
1. Given
1. EI  HF; G is the midpoint of EI; G is the midpoint of HF.
Proof:
Reasons
Statements
Example 3

14. 1.
Reasons
Proof:
Statements
1. Given A B C D
Example 3

15. Use SAS or SSS in Proofs
Write a proof.
Prove: Q  S
Example 4

16. Use SAS or SSS in Proofs
1. Given
Reasons
Statements
Example 4

17. Choose the correct reason to complete the following flow proof.B C D
A. Segment Addition Postulate
B. Symmetric Property
C. Midpoint Theorem
D. Substitution
Example 4