Question

If the diagonals of a quadrilateral divide each other proportionally, prove that it is a trapezium

Answer 1

Hi, dear

Here is your answer!!

Step-by-step explanation:

In triangle AOB and triangle COD

AO/OC = BO/OD (given)

angle AOB = angle COD (vertically opposite angle)

Therefore, triangle AOB congruent triangle COD (By SAS congruence rule)

angle ABD = angle BDC

and

angle BC = angle ACB

Since, a pair of alternate interior angles are equal.

AB parallel CD

Therefore, ABCD is a trapezium.