Question

Which properties belong to all isosceles triangles? Check all that apply.

Answer 1

Answers:
The base angles are congruent. 
The two sides opposite the base angles are congruent.
The bisector of the vertex angle is the perpendicular bisector of the base.
Explanation:
An isosceles triangle is defined as a triangle which has two equal sides and consequently two equal angles

Let's check the choices:
The base angles are congruent: Correct as mentioned above
All three angles are congruent.: Incorrect as we mentioned that only two angles are equal. An equilateral triangle is the one having three equal angles
The two sides opposite the base angles are congruent: correct as mentioned above
All three sides are congruent: Incorrect as we mentioned that only two sides are equal. An equilateral triangle is the one having three equal sides
The bisector of the vertex angle is the perpendicular bisector of the base: correct as when bisecting the isosceles triangle, two congruent right triangles are formed

Hope this helps :)

Answer 2

The base angles are congruent.

The two sides opposite the base angles are congruent.

The bisector of the vertex angle is the perpendicular bisector of the base.