Question

The vertex angle of isosceles is triangle ABC is angle C. What can you prove? Select all that apply.

A. AB = BC
B. angle A = angle B
C. angle B = angle C
D. segment BC = segment AC
E. segment AB = segment AC
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Answer 1

Answer: A. AB = BC can be proven true.

An isosceles triangle has two equal side lengths, and since the vertex angle is angle C, it means that sides AB and BC are the equal sides.

B. angle A = angle B can be proven true.

In an isosceles triangle, since the two sides are equal, the base angles are also equal.

D. segment BC = segment AC can be proven true.

In an isosceles triangle, since the two sides are equal, the base segments are also equal.

E. segment AB = segment AC can be proven true.

In an isosceles triangle, since the two sides are equal, the base segments are also equal.

C. angle B = angle C is not true.

Because the vertex angle is angle C, and it is formed by the two base segments, so it will be different than angle B and angle A.

Explanation:

Answer 2

B, D

Explanation:

You want to know what you can prove, given that the vertex angle of isosceles triangle ABC is angle C.

Isosceles triangle

A triangle is isosceles if it has two congruent sides or two congruent angles. In either case, the angles opposite the congruent sides are congruent, and vice versa.

The vertex angle is opposite the "base" of the isosceles triangle. The sides of the vertex angle are the congruent sides, and the angles that are not the vertex angle are the congruent angles.

A. AB = BC

These sides share point B, which is not the vertex. This cannot be proven.

B. Angle A = Angle B

These are the base angles of the triangle, hence congruent. This can be proven.

C. Angle B = Angle C

These angles cannot be proven congruent using the given information. This will be true if and only if the isosceles triangle is also an equilateral triangle.

D. BC = AC

These sides share point C, which is the vertex. This can be proven.

E. AB = AC

These sides share point A, which is not the vertex. This cannot be proven.