Standard
G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Rhombuses, rectangles, and squares are all parallelograms that have special properties about them.
It is a parallelogram with four congruent sides (equilateral).
If a parallelogram is a rhombus, then the diagonals form a right angle.
If a parallelogram is a rhombus, then the diagonals bisect a pair of opposite angles.
It is a parallelogram with four right angles (equiangular).
The diagonals of a rectangle are congruent. So AC = BD.
It is a parallelogram with four right angles and four congruent sides.
Remember that these are all parallelograms so they still have the properties that every parallelogram has! Here's a little summary of the properties:
Additional parallelogram properties:
Additional parallelogram properties:
Additional parallelogram properties: