Question

which rule explains why these triangles are congruent?

diagram of triangles vyx and vwx with markings

options:
sas
sss
asa
aas
these triangles cannot be proven congruent.

Explanation:

Step1: Identify congruent parts

In triangles \( \triangle VYX \) and \( \triangle VWX \):

• \( VY = VW \) (marked with red ticks, so these sides are congruent).
• \( \angle Y = \angle W \) (marked with red arcs, so these angles are congruent).
• \( VX = VX \) (common side, so this side is congruent for both triangles).

Step2: Match with congruence rule

The SAS (Side - Angle - Side) congruence rule 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. Here, we have two sides (\( VY = VW \), \( VX = VX \)) and the included angle (\( \angle Y=\angle W \)) congruent. So the congruence rule is SAS.

Answer:

SAS