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 a rhombus's diagonals bisect its opposite interior angles, we rely on triangle congruence. A rhombus has all sides equal; drawing a diagonal creates two triangles with shared sides, so they are congruent via SSS. Using CPCTC, the split angles from each vertex are congruent, meaning the diagonal bisects the angle. Options B, C, and D do not address angle bisection directly: B refers to triangle angle sum, C to exterior angle sum, and D to vertical angles and supplementary angles, which are irrelevant to this proof.

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.