Question

triangles krb and zxb are shown, where (overline{rb}congoverline{bx}) and (angle krbcongangle zxb). what congruence postulate or theorem can be used to justify (\triangle krbcong\triangle zxb)?
○ side - side - side congruence postulate
○ side - angle - side congruence theorem
○ angle - side - angle congruence postulate
○ angle - angle - side congruence theorem

Explanation:

Step1: Recall Congruence Theorems/Postulates

• SSS (Side - Side - Side) Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
• SAS (Side - Angle - Side) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
• ASA (Angle - Side - Angle) Theorem: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
• AAS (Angle - Angle - Side) Theorem: If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the triangles are congruent.

We are given that \(\overline{RB}\cong\overline{BX}\) (a side) and \(\angle KRB\cong\angle ZXB\) (an angle). Also, \(\angle R B K\) and \(\angle X B Z\) are vertical angles, so \(\angle RBK\cong\angle XBZ\) (another angle).

Step2: Identify the Congruence Criterion

Since we have two angles (\(\angle KRB\cong\angle ZXB\) and \(\angle RBK\cong\angle XBZ\)) and a non - included side (\(\overline{RB}\cong\overline{BX}\)), the AAS (Angle - Angle - Side) Congruence Theorem is applicable.

Answer:

Angle - Angle - Side Congruence Theorem