Question

The diagnols of a quadrilateral ABCD intersect each other at the point O such that AO/BO=CO/DO show that ABCD is a trapezium (CHAPTER TRAINGLES class 10)

Answer 1

Hi, we require to prove that ABCD is a trapezium
Given- AO/BO =CO/DO and o is the centre of the quadrilateral.
TO PROVE - ABCD is a trapezium.
PROOF - construct point E on the side AD from o.
then, according to BPT,
AE/ED=AO/BO ........1
AE/ED = CO/DO.......2
FROM eq. 1 and 2 we get
AO/BO = CO/DO
EO parallel to AB
eo parallel to AC
ABCD is a trapezium
H. P
HOPE IT HELPS