CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The diagonals of a quadrilateral ABCD intersect each other at the point O such that AOBO=CODO. Show that ABCD is a trapezium.

Open in App
Solution

Given:
The diagonals of a quadrilateral ABCD intersect each other at the point O such that AOBO=CODO
i.e.,
AOCO=BODO
To Prove: ABCD is a trapezium
Construction:
Draw OEDC such that E lies on BC.
Proof:
In BDC,
By Basic Proportionality Theorem,
BOOD=BEEC............(1)
But, AOCO=BODO (Given) .........(2)
From (1) and (2)
AOCO=BEEC
Hence, By Converse of Basic Proportionality Theorem,
OEAB
Now Since, ABOEDC
ABDC
Hence, ABCD is a trapezium.
493944_465426_ans_cabefe8118804d8488defd358ac22780.png

flag
Suggest Corrections
thumbs-up
5
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Trapezium
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon