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? - Mathematics

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.