Question

1. these triangles can be proven congruent using which postulate? diagram of two triangles: one with sides 5, 11 and a 137° angle; the other with sides 5, 11 and a 137° angle options: sss congruence postulate, sas congruence postulate, asa congruence postulate, ssa congruence postulate

Explanation:

To determine the congruence postulate, we analyze the given triangles:

• One side has length 5, another has length 11, and the included angle is \(133^\circ\) for both triangles.
• The SAS (Side - Angle - Side) Congruence Postulate states that 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.
• SSS requires all three sides to be congruent, ASA requires two angles and the included side, and SSA is not a valid congruence postulate (it does not guarantee triangle congruence in all cases). So, the SAS Congruence Postulate applies here.

Answer:

SAS Congruence Postulate