Question

no spamming.......................​

Answer 1

Given:

The diagonals of a quadrilateral ABCD intersect each other at the point O such that BOAO=DOCO

i.e., COAO=DOBO

To Prove: ABCD is a trapezium

Construction:

Draw OE∥DC such that E lies on BC.

Proof:

In △BDC,

By Basic Proportionality Theorem,

ODBO=ECBE............(1)

But, COAO=DOBO (Given) .........(2)

∴ From (1) and (2)

COAO=ECBE

Hence, By Converse of Basic Proportionality Theorem,

OE∥AB

Now Since, AB∥OE∥DC

∴ AB∥DC

Hence, ABCD is a trapezium.

☺️hope it helps you

Answer 2

please refer to these three pictures

HOPE IT HELPS YOU

MARK ME AS BRAINLIEST PLEASE