Question

1. are the below triangles congruent? *

yes by sss
yes by sas
yes by asa
yes by aas
no

Explanation:

Step1: Identify matching sides/angles

In the triangles:

• One pair of sides (double hash marks) are congruent: $side_1 \cong side_1'$
• One pair of sides (single hash marks) are congruent: $side_2 \cong side_2'$
• The included angle between these sides is congruent (marked angle, vertical angles are equal): $\angle \cong \angle'$

Step2: Match to congruence rule

The SAS (Side-Angle-Side) 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, the triangles are congruent. This matches the given triangles.

Answer:

Yes by SAS