Answer:
(b) Yes, they are congruent
Explanation:
Given two triangles with a side length marked as 5 units, you want to know whether they are congruent. One triangle has marked angles 65° and 67° with the angle opposite the marked side being unmarked. The other triangle has angles marked 65° and 48°, with the latter being opposite the marked side.
Third angle
In each case, the sum of angles is 180°, so the measure of the third angle is the value that makes that be the sum of all angles.
Triangle 1:
The third angle is 180° -65° -67° = 48°.
Triangle 2:
The third angle is 180° -65° -48° = 67°.
Similarity
The measures of the angles in each triangle are 48°, 65°, and 67°. Since the angles are the same, the triangles are similar.
Congruence
In each case, the marked side is opposite the smallest angle. This means we can claim congruence using either the ASA or AAS postulates.
Yes, they are congruent.