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.

Step-by-step 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

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.