Question

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

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

Answer 1

the opposite angles are equal

i.e. i) < A = <C ii) < B = < D

the opposite sides are equal that is

i)AB =CD

ii) AD= BC

the diagonals bisect each other

i) AO=OC

ii)BO=OD

the adjacent angle are supplementary . that is

i)<D + < C=180 DEGREE

ii)<A+<D=180degree

iii)<B+<C=180 degree

Explanation:

Answer 2

Explanation:

the opposite angles are equal

i.e. i) < A = <C ii) < B = < D

the opposite sides are equal that is

i)AB =CD

ii) AD= BC

the diagonals bisect each other

i) AO=OC

ii)BO=OD

the adjacent angle are supplementary . that is

i)<D + < C=180 DEGREE

ii)<A+<D=180degree

iii)<B+<C=180 degree