ABCD is a trapezium in which AB ||DC and P and Q are points on AD and BC, respectively such that PQ || DC. If PD = 18 cm, BQ = 35 cm, and QC = 15 cm, find AD.
Answer : [AD=60cm]
Given:- ABCD is a trapezium in which AB || DC, P, and Q are points on AD and BC. Such that PQ || DC.
PD = 18 cm, BQ = 35, QC = 15 cm
To prove:- Find AD
Proof:-
Construction:- Join BD
In ABD, PO || AB
We know that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then according to basic proportionality theorem the other two sides are divided in the same ratio.
In BDC, OQ || DC
Similarly by using the basic proportionality theorem.
from equation (1) and (2) we get