Question

90 POINTS!!!!!!!!!!!!!!!How do you prove each of the following properties of a parallelogram?

Opposite sides are congruent.
Opposite angles are congruent.
The diagonals of a parallelogram bisect each other.
If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.
Rectangles are parallelograms with congruent diagonals.

Answer 1

Except last rectangle one rest have same process of proving.

The simplest way is

• Take a sample parallelogram
• Then break into two triangles
• Then use SSS or SAS etc to prove the triangles are congruent
• Then just everything is similar so all are proved.

For the last one

• Take a rectangle
• Define that opposite sides are equal then opposite pairs of angles are equal .