Warm-Up Find the value of x: 30° 40° x° x° 35° 25° 74° 44° x°

Prove Triangles Congruent by SSS and SAS

Postulate 19 Side-Side-Side (SSS) Congruence Postulate: If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. B If side AB = RS, side BC = ST, side CA = TR, then ∆ABC ≅ ∆RST ˜ ˜ ˜ A S C R T

Side-Angle-Side (SAS) Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. R If side RS = UV, angle R = U, and side RT = UW, then RST = UVW ˜ ˜ ˜ T U S ˜ W V

Example 1 Statement Reason Given AB = CD, AD = CB AC = AC ∆ABC = ∆CDA Prove ∆ABC ≅ ∆CDA. A B D C Statement Reason Given AB = CD, AD = CB AC = AC ∆ABC = ∆CDA ˜ ˜ Reflexive Property ˜ ˜ SSS = Postulate ˜

Example 2 Determine whether the congruence statement is true. Explain your reasoning. ∆XYZ = ∆RST ˜ Y TRUE SSS X Z S R T

Example 3 Determine whether the congruence statement is true. Explain your reasoning. ∆ABC = ∆DCB ˜ A 8 B NOT TRUE 5 10 4 BD = CA D C 8

Example 4 ˜ ˜ Statement Reason MP= NP OP bisects MPN MPO = NPO OP = OP Prove MOP = NOP. Given MP = NP, OP bisects MPN. ˜ ˜ M N O P Statement Reason MP= NP OP bisects MPN MPO = NPO OP = OP MOP = NOP ˜ Given Given Def. of bisector Reflexive Property ˜ SAS = Postulate ˜ ˜

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