Question

In the given figure, ABCD and PQRC are rectangles and Q is the mid-point of AC. Prove that

(i) DP = PC

(ii) PR = $\frac{1}{2}$ AC

Answer 1

Rectangles ABCD and PQRC are given as follows:

Q is the mid-point of AC.

In , Q is the mid-point of AC such that

Using the converse of mid-point theorem, we get:

P is the mid-point of DC

That is;

Similarly, R is the mid-point of BC.

Now, in , P and R are the mid-points of DC and BC respectively.

Then, by mid-point theorem, we get:

Now, diagonals of a rectangle are equal.

Therefore putting ,we get:

Hence Proved.