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Concept 1

Concept 1. ___. ___. ___. ___. Given: QU  AD , QD  AU. Use SSS to Prove Triangles Congruent. Write a flow proof. Prove: Δ QUD  Δ ADU. Example 1. Use SSS to Prove Triangles Congruent. Answer: Flow Proof:. Example 1. A B C D.

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Concept 1

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  1. Concept 1

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

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

  4. A B C D Which information is missing from the flowproof?Given: AC ABD is the midpoint of BC.Prove: ΔADC  ΔADB ___ ___ ___ ___ A.AC  AC B.AB  AB C.AD  AD D.CB  BC ___ ___ ___ ___ ___ ___ 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. By definition of congruent segments, all corresponding segments are congruent. Therefore, ΔWDV  ΔMLP by SSS. Example 2 ANS

  10. A B C Determine whether ΔABCΔDEFfor 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 Example 2A

  11. Concept 2

  12. 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. Use SAS to Prove Triangles are Congruent Example 3

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

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

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

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

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

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