4-5 Proving Congruence Included side: the side between the 2 angles used. AB is the included side between angles A and B. BC is the included side between angles B and C. AC is the included side between angles A and C. B A C

Construction Page 234 Materials: Paper, straightedge, compass Constructing congruent triangles using two angles and included side

Postulate 4.3 ASA (angle-side-angle) If two angles and the included side of one triangle are congruent to the corresponding angles and the included side of another triangle, then the triangles are congruent. B E DEF  ABC A C D F

Example #1 In DEF and ABC, D  C, E  A and DE  CA. Write a congruence statement for the two triangles. DEF  CAB OR FDE  BCA EDF  ACB Proof: Check Your Progress #1 p. 235

Theorem 4.5 – AAS (angle-angle-side) If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent. B E DEF  ABC A C D F

Example #2 ABC and FDE each have one pair of sides and one pair of angles marked to show congruence. What other pair of angles needs to be marked so the two triangles are congruent by AAS? B E A & F A C D F

Examples 3 & 4 Determine whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. SAS ASA

Concept Summary Homework #27 p. 239 7, 8, 13, 14, 16, 20-22, 27-28