Q8 of 31 Page 4

Construct a quadrilateral PQRS in which QR = 7.5 cm, RP = PS = 6 cm, RS = 5 cm and QS = 10 cm.

Steps of construction:
1. Draw QR = 7.5 cm.
2. With Q as centre and QS (= 10 cm) as radius draw an arc.
3. With R as centre and RS (= 5 cm) as radius draw an arc to cut the arc of step 2 at S.
4. With R and S as centre and radius 6 cm draw two arcs to cut each other at P.
5. Join PQ, PS and SR.PQRS is the required quadrilateral.

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6 Construct a quadrilateral ABCD in which AB = 7 cm, AD = 6 cm, AC = 7 cm, BD = 7.5 cm and BC = 4cm. 7 Construct a quadrilateral ABCD in which AB = CD = 3 cm, BC = 2.5 cm, AC = 4 cm and BD = 5 cm. 9 Construct a quadrilateral ABCD in which BC = 5.5 cm, CD = 4 cm, ∠ A = 70°, ∠ B = 110° and ∠ D = 85°. 10 Is it possible to construct a quadrilateral ABCD in which AB = 5 cm, BC = 7.5 cm, ∠ A = 80°, ∠ B = 140° and ∠ C = 145°? If not, give reason.