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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 :

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 .

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