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.
To Prove: ABCD is a trapezium or AB CD.
Construction: Draw line EO to AB touching BC at F.
In ABD, EO AB.
Therefore, by Basic Proportionality Theorem, we get
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.