Answer (a) :
These triangles are congruent under the SAS congruence criterion. The angles that face each other at the tip of these two triangles are vertically opposite angles, so their measures will be equal. It is already given that two sides of these two angles are equal. Since two sides and one included angle is equal, the SAS congruence criterion can be used to prove that this triangle is congruent.
Answer (b) :
These triangles are congruent under the SSS congruence criterion. This criterion states that if all three sides of two triangles are equal then they are congruent triangles. Since two sides and one included/common side of these triangles are equal they can said to be congruent under the SSS congruence criterion.
Answer (c) :
These triangles can be proved to be congruent using the SAS congruence criterion. Let us prove it using the following steps :
Given :
In triangle 1 :
- Measure of an angle = 48°
- Measure of one of its side = 6 cm
- Measure of another side = 6 cm
In triangle 2 :
- Measure of an angle = 48°
- Measure of one it's side = 6 cm
- Measure of another side = 6 cm
Since two sides and one included angles of both these triangles are equal, we can conclude that they are congruent under the SAS congruence criterion.