Prove that the segments joining the midpoints of the opposite sides of a quadrilateral bisect each other.

Refer to the attached image.

Given: A quadrilateral ABCD, where P, Q, R and S are the mid points of the sides AD, AB, BC, CD respectively.

To prove: The segments joining the mid points of the opposite sides of a quadrilateral bisect each other that is OP=OR and OQ=OS.

Proof: Join the segment BD.

Consider the triangle ABD,

Since P is the mid point of AD and Q is the mid point of AB.

Therefore, .... (Equation 1)

[Line segments joining the mid points of two sides of a triangle is parallel to the third side and is also half of it]

Consider the triangle BCD,

Since S is the mid point of CD and R is the mid point of BC.

Therefore, .... (Equation 2)

[Line segments joining the mid points of two sides of a triangle is parallel to the third side and is also half of it]

By equations 1 and 2, we get

Therefore, PQRS is a parallelogram as opposite sides are equal and parallel.

In a parallelogram, diagonals bisect each other.

Since, PR and QS are the diagonals of the parallelogram PQRS.

Therefore, OP=OR and OQ=OS.

Hence, proved.

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)