Concept 1

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

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

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

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

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

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

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

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

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

Concept 2

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

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

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

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

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

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