QUESTION
Construct ☐ PQRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m∠Q = 110° , m∠R = 70° . If it is given that ☐ PQRS is a parallelogram, which of the given information is unnecessary?
SOLUTION
Steps of Construction:
Step 1: Draw QR = 5.6 cm.
Step 2: Draw ∠TQR = 110° .
Step 3: With Q as centre and radius 3.5 cm, draw an arc cutting ray QT at P.
Step 4: Draw ∠QRV = 70° .
Step 5: With R as centre and radius 3.5 cm, draw an arc cutting ray RV at S.
Step 6: Join PS.
Here, PQRS is the required quadrilateral.
Since, the opposite sides of a parallelogram are congruent.
∴ Either l(PQ) or l(SR) is required.
To construct a parallelogram lengths of adjacent sides and measure of one angle is required.
∴ Either l(PQ) and m∠Q or l(SR) and m∠R is the unnecessary information given in the question.
