In triangle ABC, if AB equals AC, what is the type of triangle and what can you say about the angles at B and C?

Prepare for the Geometry CBE Exam with targeted resources. Access interactive quizzes and detailed explanations to master geometric concepts effectively and excel in your test!

Multiple Choice

In triangle ABC, if AB equals AC, what is the type of triangle and what can you say about the angles at B and C?

Explanation:
When two sides in a triangle are equal, that triangle is isosceles and the line BC is considered the base. Since AB equals AC, vertex A is the apex and BC is the base. In an isosceles triangle, the base angles are congruent, so the angles at B and C are equal. Therefore, the triangle is isosceles and the angles at B and C are equal. The other possibilities require conditions not given: an equilateral triangle would need all three sides equal, a scalene triangle would require all sides different, and a right triangle would require a 90-degree angle.

When two sides in a triangle are equal, that triangle is isosceles and the line BC is considered the base. Since AB equals AC, vertex A is the apex and BC is the base. In an isosceles triangle, the base angles are congruent, so the angles at B and C are equal. Therefore, the triangle is isosceles and the angles at B and C are equal. The other possibilities require conditions not given: an equilateral triangle would need all three sides equal, a scalene triangle would require all sides different, and a right triangle would require a 90-degree angle.

More practice questions