Proving Triangles Congruent – SSS, SAS LESSON 4–4 Proving Triangles Congruent – SSS, SAS

Write a congruence statement for the triangles. A. ΔLMN  ΔRTS B. ΔLMN  ΔSTR C. ΔLMN  ΔRST D. ΔLMN  ΔTRS 5-Minute Check 1

Name the corresponding congruent angles for the congruent triangles. A. L  R, N  T, M  S B. L  R, M  S, N  T C. L  T, M  R, N  S D. L  R, N  S, M  T 5-Minute Check 2

Name the corresponding congruent sides for the congruent triangles. A. LM  RT, LN  RS, NM  ST B. LM  RT, LN  LR, LM  LS C. LM  ST, LN  RT, NM  RS D. LM  LN, RT  RS, MN  ST ___ 5-Minute Check 3

Refer to the figure. Find x. A. 1 B. 2 C. 3 D. 4 5-Minute Check 4

Refer to the figure. Find m A. B. 39 C. 59 D. 63 5-Minute Check 5

Given that ΔABC  ΔDEF, which of the following statements is true? A. A  E B. C  D C. AB  DE D. BC  FD ___ 5-Minute Check 6

You proved triangles congruent using the definition of congruence. Use the SSS Postulate to test for triangle congruence. Use the SAS Postulate to test for triangle congruence. Then/Now

included angle Vocabulary

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

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 ___ Example 1 CYP

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  FH, and G is the midpoint of both EI and FH. Example 3

A. Reflexive B. Symmetric C. Transitive D. Substitution The two-column proof is shown to prove that ΔABG  ΔCGB if ABG  CGB and AB  CG. Choose the best reason to fill in the blank. 1. Reasons Proof: Statements 1. Given 2. ? Property 2. 3. SSS 3. ΔABG ΔCGB A. Reflexive B. Symmetric C. Transitive D. Substitution Example 3

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

Proving Triangles Congruent – SSS, SAS LESSON 4–4 Proving Triangles Congruent – SSS, SAS