Construction of Polygons
- Construction of quadrilateral when one angle and four sides are given:
Construct a quadrilateral PQRS with PQ = 6 cm, QR = 7 cm, RS = 8.5 cm, PS = 6.5 cm and ∠Q = 90°.
Step 1: Draw line segment PQ of length 6 cm.
Step 2: Draw ∠XQP = 90° at point Q.
Step 3: Taking Q as centre and 7 cm as radius, mark an arc on QX and name the point of intersection as R.
Step 4: Taking R as centre and 8.5 cm as radius, mark an arc.
Step 5: Taking P as centre and 6.5 cm as radius, mark an arc. Let it intersect the previous arc at point S.
Step 6: Join PS and RS.
PQRS is the required quadrilateral.
- Construction of a quadrilateral when three sides and two included angles are given
Construct a quadrilateral PQRS with SR = 6.5 cm, PS = 5 cm, QR = 3 cm, ∠R = 120°, and ∠S = 70°.
The steps of construction are as follows:
Draw SR = 6.5 cm. Draw ∠SRX = 120° at R and ∠RSY = 70° at S.
With S as centre, draw an arc of radius 5 cm intersecting SY at P.
With R as cen…
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