Question

Two of the corresponding angles and the included sides of two triangles are

congruent. Which statement must be true regarding the triangles?
A. The triangles are equilateral.
B. The triangles are isosceles.
C. The triangles are congruent.
D. The triangles have at least one right angle.

Answer 1

C. The triangles are congruent.

Explanation:

By the ASA criterion, the two triangles must be congruent.

Answer 2

C

Explanation:

A. Equilateral triangle is a triangle with all sides congruent. These triangles are not equilateral, because there is no information about all three sides of each triangle.

B. Isosceles triangle is a triangle with two sides congruent. These triangles are not isosceles, because there is no information about congruence of two sides of each triangle.

C. ASA posrulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. This is exactly what you are given in this question, so this option is true.

D. This option is false, because triangles can have two pairs of congruent angles (for example, 20° and 40°), then third pair are also congruent angles not necessarily right (180°-20°-40°=120°≠90°).