4.3 Analyzing Triangle Congruence. Objectives. Identify and use the SSS, SAS, and ASA Congruence Postulates and the AAS and HL Congruence Theorems. Use counterexamples to prove that other side and angle combinations cannot be used to prove triangle congruence. 4.3 Analyzing Triangle Congruence.
AAS (Angle-Angle-Side) Congruence Theorem 4.3.1: If two angles and a nonincluded
side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.
HL (Hypotenuse-Leg) Congruence Theorem
4.3.2: If the hypotenuse and a leg of a right
triangle are congruent to the hypotenuse and
a leg of another right triangle, then the two triangles are congruent.
4.3 Analyzing Triangle CongruenceKey Skills
Use AAS and HL Theorems to determine
whether triangles are congruent.
by HL Theorem.
c. PRS may not be congruent to ONM
because triangles cannot be proven congruent by SSA.