Question

which rule explains why these triangles are congruent?
sas
aas
sss
asa
these triangles cannot be proven congruent.

Explanation:

Step1: Recall congruence rules

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

Step2: Analyze the given triangles

In the given triangles, we have two sides and the included angle marked as equal. For example, if we consider the sides and the angle between them (the marked angle) in each triangle, we can see that the \(SAS\) (Side - Angle - Side) congruence rule is satisfied.

Answer:

SAS