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

Question

is calculation needed? i guess so...

Answer 1

rectangle = ABCD
then the triangles
ABC and BCD are congruent.

Answer 2

To prove this you need to show that the line segements joining the midpoints of the opposite sides have the same midpoint.

For the quadrilateral ABCD, AB and CD are opposite sides and so are AD and BC.
________

The midpoint of AB is M1(A + B)/2.
The midpoint of CD is M2(C + D)/2.
The midpoint of M1M2 is
(M1 + M2)/2 = [(A + B)/2 + (C + D)/2]/2 = (A + B + C + D)/4
________

The midpoint of AD is N1(A + D)/2.
The midpoint of BC is N2(B + C)/2.
The midpoint of N1N2 is
(N1 + N2)/2 = [(A + D)/2 + (B + C)/2]/2 = (A + B + C + D)/4
______________

The two lines have the same midpoint. Therefore they bisect each other.

Answer 3

well if your doing like a proof (statement/reason) it would be that the sides would be bisected by the line segments because the midpoint divides a line into two equal segments