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Step 5: With B as centre and radius = 3.7 cm, draw an arc.

Step 6: With D as centre and radius = 2.9 cm, draw an arc to intersect the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.

When Three Sides and Two Diagonals are Given

Let us construct a quadrilateral BEST in which BE = 3 cm, ES = 2.5 cm, BT = 3.5 cm,
BS = 4 cm, ET = 5 cm.
First, we draw the rough sketch of quadrilateral and mark the given measurements
of sides and diagonals.

Steps of construction:
Step 1: Draw a line segment BE = 3 cm.

Step 2: With B as centre and radius equal to 4 cm, draw an arc.
Step 3: With E as centre and radius equal to 2.5 cm, draw another arc,
cutting the previous arc at S.
Step 4: Join ES and BS.

Step 5: With B as centre and radius equal to 3.5 cm, draw an arc.
Step 6: With E as centre and radius equal to 5 cm, draw another arc, cutting
the previous arc at T.

Step 7: Join BT, ET and ST.
Thus, BEST is the required quadrilateral shown alongside.

When Two Adjacent Sides and Three Angles are Given

Let us construct a quadrilateral ROAD in which RO = 4.5 cm, OA = 2 cm, ∠R
= 45°, ∠O = 135° and ∠A = 90°.
Draw a rough sketch of quadrilateral ROAD and mark its measurements.

Steps of construction:
Step 1: Draw a line segment RO = 4.5 cm.

Step 2: At R, construct ∠XRO = 45°.
Step 3: At O, construct ∠YOR = 135°.
Step 4: With centre O and radius equal to 2 cm, draw an arc
cutting OY at A.

Step 5: At A, construct ∠ZAO = 90°, so that ZA and XR intersect
at D.
Thus, ROAD is the required quadrilateral.

Think and Answer

Is it possible to construct a quadrilateral PQRS in which PQ = 4 cm, QR = 5 cm, ∠Q = 120°, ∠P
= 105° and ∠R = 135°? If not, why?

77 Quadrilaterals