What are some proofs that could be used to prove that a given rhombus is a square?

Question

Avery Allen · Accepted Answer

Both a rhombus and a square have equal sides, so in order to prove that a rhombus is a square ...

1) If all four interior angles equal 90 degrees , the rhombus must be a square. OR 2) If the diagonals are equal , then the rhombus must be a square. Hope that helped

Aaliyah Anderson · Answer

undefined To prove that a given rhombus is a square, you can use the following proofs:

1. Show that all angles of the rhombus are right angles. Since a square has four right angles, if you can demonstrate that all angles in the rhombus are right angles, then it must be a square.

2. Prove that all sides of the rhombus are congruent. If you can show that all sides of the rhombus are equal in length, then it is a square because a square has four congruent sides.

3. Demonstrate that the diagonals of the rhombus are congruent and perpendicular bisectors of each other. In a square, the diagonals are not only congruent but also perpendicular bisectors of each other. If you can prove this property for the rhombus, it must be a square.

Using any of these proofs or a combination of them can establish that a given rhombus is indeed a square.