Question

select the correct answer.
how can you justify that the diagonals of a rhombus bisect opposite interior angles?
a. show that the diagonals form two congruent triangles using the definition of a rhombus and geometric properties. then, use cpctc (corresponding parts of congruent triangles are congruent) to show that the opposite interior angles are bisected.
b. show that the interior angles of each triangle created by the diagonals must add to 180°.
c. show that the exterior angles of the rhombus must sum to 360°.
d. show that the vertical angles created by the diagonals are congruent. then, show that the opposite interior angles are supplementary to these angles.

Explanation:

To justify that the diagonals of a rhombus bisect opposite interior angles, we need to use geometric properties related to congruent triangles. A rhombus has all sides equal. When we consider the diagonals, we can show that the triangles formed are congruent (using SSS - side - side - side congruence as all sides of the rhombus are equal and the diagonal is common). Then, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), we can establish that the angles are bisected. Option B only mentions the sum of interior angles of a triangle (a general property not specific to angle - bisecting in a rhombus). Option C is about exterior angles (not relevant to angle - bisecting by diagonals). Option D involves vertical angles and supplementary angles (not directly showing angle - bisecting).

Answer:

A. Show that the diagonals form two congruent triangles using the definition of a rhombus and geometric properties. Then, use CPCTC (corresponding parts of congruent triangles are congruent) to show that the opposite interior angles are bisected.