Question

triangle congruence criteria
score: 14/15 penalty: none
question
determine the relationship between the two triangles and whether or not they can be proven to be congruent
answer attempt 1 out of 3
the two triangles are related by , so the triangles

Explanation:

Step1: Identify marked congruent parts

Both triangles have a right angle ($90^\circ$), one pair of single-marked congruent legs, and one pair of double-marked congruent legs.

Step2: Match to congruence criterion

For right triangles, if two legs of one triangle are congruent to the two legs of another right triangle, the SAS (Side-Angle-Side) congruence criterion applies (the right angle is the included angle between the legs).

Step3: Conclude congruence

Since the two pairs of corresponding legs are congruent and the included right angles are congruent, the triangles meet the SAS condition for congruence.

Answer:

The two triangles are related by SAS (Side-Angle-Side) congruence, so the triangles can be proven congruent.