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

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

Use SSS to Prove Triangles Congruent Statement Reason Example 1

Statement Reason

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

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

Statement Reason

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. SAS Postulate 3. ΔABG ΔCGB A. Reflexive B. Symmetric C. Transitive D. Substitution Example 3

Statement Reason Write a 2-Column proof. Prove: Q  S Use SAS or SSS in Proofs Write a 2-Column proof. Prove: Q  S Statement Reason Example 4

coordinate geometry. You must show work! SSS on the Coordinate Plane 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. Prove the triangles are congruent by SSS using coordinate geometry. You must show work! Example 2A

SSS on the Coordinate Plane (Coordinate Geometry) Example 2C