Question

Construct a parallelogram PQRS given PQ=5cm, QR=3cm, PR=6cm​

Answer 1

See attached diagrams.

Explanation:

In a parallelogram, opposite sides are parallel and equal in length.

Therefore, if PQRS is a parallelogram, then PQ ║ SR and QR ║ SP, and PQ = SR and QR = SP.

Given PQ = 5 cm, then SR = 5 cm.

Given QR = 3 cm, then SP = 3 cm.

The diagonals of the parallelogram are PR and QS and bisect each other.

To construct parallelogram PQRS, follow these steps:

Diagram 1

• Draw a line labeled PQ that measures 5 cm.
• Draw a circle with a radius of 6 cm and a center at P.
• Draw a circle with a radius of 3 cm and a center at Q.
• Mark one of the points of intersection of the two circles as point R.
• Connect points Q and R with a straight line segment.

Diagram 2

• Draw a circle with a radius of 5 cm and a center at R.
• Draw a circle with a radius of 3 cm and a center at P.
• Mark the point of intersection of the two circles (on the same side of PQ as point R) as point S.

Diagram 3

• Connect points R and S with a straight line segment.
• Connect points S and P with a straight line segment.