CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.2 Question 10
10. The diagonals of a quadrilateral ABCD intersect each other at the point O such that
. Show that ABCD is a trapezium.
Solution:
Given:
(1)
To Prove: ABCD is a trapezium or AB
CD.
Construction: Draw line EO
to AB touching BC at F.
Proof:
In
ABD, EO
AB.
Therefore, by Basic Proportionality Theorem, we get
(2)
From (1) and (2), we get
Therefore, by Converse of Basic Proportionality theorem, we get
EO
DC. (3)
But, we also have EO
AB (By construction) (4)
Therefore, from (3) and (4), we have AB
DC which means ABCD is a trapezium.
Hence Proved.
Rudra Prasad Nayak says
helped me a lot in completing my course
pratiyaksh says
Very helpful