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Question
Construct a quadrilateral PQRS, in which PQ = 4 cm, QR = 5 cm, ∠P = 50°, ∠Q = 110° and ∠R = 70°.
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Solution
\[\text { Steps of construction: }\]
\[\text { Step I: Draw PQ = 4 cm }. \]
\[\text { Step II: Construct } \angle XPQ = 50^\circ \text { at P and } \angle PQY = 110^\circ \text { at Q }. \]
\[\text { Step III : With Q as the centre and radius 5 cm, cut off QR = 5 cm } . \]
\[\text { Step IV: At R, draw } \angle QRZ = 70^\circ \text { such that it meets PX at S } . \]
The quadrilateral so obtained is the required quadrilateral .
RELATED QUESTIONS
Construct the following quadrilaterals.
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MO = 6 cm
OR = 4.5 cm
∠M = 60°
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Construct a quadrilateral ABCD in which AB = 3.8 cm, BC = 3.4 cm, CD = 4.5 cm, AD = 5 cm and ∠B= 80°.
Construct a quadrilateral ABCD in which AB = BC = 3 cm, AD = CD = 5 cm, and ∠B = 120°.
Construct a quadrilateral PQRS, in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ∠Q = 75° and ∠R = 120°.
Construct a quadrilateral ABCD, in which AD = 3.5 cm, AB = 4.4 cm, BC = 4.7 cm, ∠A = 125° and ∠B= 120°.
Construct a quadrilateral PQRS, in which ∠Q = 45°, ∠R = 90°, QR = 5 cm, PQ = 9 cm and Rs = 7 cm.
Construct a quadrilateral BDEF, where DE = 4.5 cm, EF = 3.5 cm, FB = 6.5 cm, ∠F = 50° and ∠E = 100°.
Construct the following quadrilaterals with the given measurements and also find their area.
AGRI, AG = 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°
A quadrilateral can be constructed uniquely if three angles and any two sides are given.
