Essay
Your teacher will grade your response for question 11 to ensure that you receive proper credit for your answer.
ABCD is a rhombus. Explain why Triangle A B C is congruent to triangle C D A.
A rhombus is shown. Point A is in the upper right. Point B is in the upper left. Point C is in the lower right. Point D is in the lower left. The diagonal between A and C is drawn.
Triangle ABC is congruent to triangle CDA because they both have the same side lengths and angles.
In a rhombus, all four sides are equal in length. Therefore, side AB is equal to side CD. Additionally, both triangles share side AC, which is a diagonal of the rhombus.
Furthermore, the angles in triangle ABC are congruent to the angles in triangle CDA. In a rhombus, opposite angles are equal. Thus, angle ABC is congruent to angle CDA, and angle BAC is congruent to angle CAD.
Therefore, due to the equal side lengths and congruent angles, triangle ABC is congruent to triangle CDA.