Question

Write the proofs of the following statements. . Diagonals of a square are perpendicular bisectors of each other. • Diagonals of a rhombus bisect its opposite angles. • Diagonals of a square bisect its opposite angles.​

Answer 1

The rhombus has the following properties:
All of the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary).
All sides are congruent by definition.
The diagonals bisect the angles.
The diagonals are perpendicular bisectors of each other.
The rectangle has the following properties:
All of the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other).
All angles are right angles by definition.
The diagonals are congruent.
The square has the following properties:
All of the properties of a rhombus apply (the ones that matter here are parallel sides, diagonals are perpendicular bisectors of each other, and diagonals bisect the angles).
All of the properties of a rectangle apply (the only one that matters here is diagonals are congruent).
All sides are congruent by definition.
All angles are right angles by definition.