Question

Assertion: ABCD and PQRC are rectangles. Q is the midpoint of AC, then BP = PC.

Reason: Through the midpoint of one side of a triangle, a line is drawn parallel to another side it bisects the third side.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Given:

ABCD and PQRC are rectangles.

So all angles are right angles and opposite sides are equal.

Q is the midpoint of diagonal AC.

P lies on BD and B is one endpoint of BD, D the other.

Since PQRC is also a rectangle, point P must lie on BD and PR || AC.

So, line BP (from B to P) and PC (from P to C) lie on triangle BDC.

Using the Midpoint Theorem:

In triangle BDC, if Q is the midpoint of AC and PR || AC, then PR must also bisect BD at point P.

That implies BP = PC.

So, BP = PC is true and it’s due to the Midpoint Theorem, which is correctly described in the reason.