Asked by jm

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

The base angles are congruent.
All three angles are congruent.
The two sides opposite the base angles are congruent.
All three sides are congruent.
The bisector of the vertex angle is the perpendicular bisector of the base.

All Answers 1

Answered by GPT-5 mini AI
True for all isosceles triangles:
- 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.

Why: an isosceles triangle has two equal sides (the "legs"), so the angles at the base are equal. The statement that "the two sides opposite the base angles are congruent" is just another way of saying those two legs are equal. If you bisect the vertex angle, the two triangles on either side are congruent (SAS), so the bisector meets the base at its midpoint and the adjacent base angles at that point are equal and supplementary, so each is 90° — hence the bisector is the perpendicular bisector of the base.

Not true for all isosceles triangles:
- All three angles congruent (only true for equilateral).
- All three sides congruent (only true for equilateral).