Question

A line through P and parallel to QR bisects side AD. If True enter 1 else if False enter 0.

Answer 1

Given: ABCD is a kite shaped figure. $AB=AD$, $BC=CD$, P, Q and R are mid points of AB, BC and CD respectively
Construction: Join AC and BD. Let the line through P, parallel to QR meet AD at S.
In $△BCD$
Q is mid point of BC and R is mid point of CD
Then, $QR\parallel BD$ (mid point theorem)..(I)
Since, $PS\parallel QR$ (II)
hence, $PS\parallel BD\parallel QR$ (Form I and II)
Now, In $△ABD$
P is mid point of AB and $PS\parallel BD$
Thus, by converse of mid point theorem, $S$ is mid point of AD