State True/false:

Construction of a quadrilateral PQRS is not possible when ∠Q = 45° and ∠R = 90°, QR = 5 cm, PQ = 9 cm, and RS = 7 cm.

The given details are ∠Q = 45° and ∠R = 90°, QR = 5 cm, PQ = 9 cm, and RS = 7 cm.

Steps to construct a quadrilateral:

Step 1- Draw a line QR = 5cm

Step 2- Construct an angle of 45^o at Q.

Step 3- Cut an arc of radius 9cm with Q as the center to mark that point as P.

Step 4- Construct an angle of 90^o at R.

Step 5- Cut an arc of radius 7cm with R as the center to mark that point as S.

Step 6- Now join QP and RS.

Since the line segment QP and RS are not intersecting each other, a quadrilateral cannot be formed.