Answer:
a) congruent
b) not congruent
c) congruent
Explanation:
You want to know which sets of isosceles triangles are congruent.
Isosceles triangle
An isosceles triangle has two congruent sides and two congruent angles. If those sides and angles match corresponding sides and angles in another isosceles triangle, then the triangles will be congruent.
Unless the triangle is equilateral, the two congruent base angles will have different measures than the angle between the congruent sides. Once any of the angle measures is known, the others are determined—provided that we also know which angle it is that is known.
a) Third angle known
The congruent side measures are the same, and the apex angle is the same. This triangle pair is congruent.
b) Angles given
The base angle of one triangle is the same measure as the apex angle of the other. (Neither is 60°.) These triangles cannot be congruent.
c) Base angle known
The congruent side measures are the same, and the base angles are the same. This triangle pair is congruent.