# construct a triangle PQR in which QR=6cm and angle Q = 60degree and PR-PQ=2cm.

We have to construct a triangle with the given data as-

Step-1: Draw the base line segment QR= 6 cm.

Step-2 : From Q, draw an angle of using compass, say ∠XQR.

Step-3 :Extend the line QX in the opposite direction as well to T. Cut a line segment QS of 2 cm from the line segment QT  extended in the opposite side of line segment XQ. Now join the point to R in order to get SR.

Step-4 : Draw perpendicular bisector AB of line segment SR. Let it intersect QX at point P. Join PQ, PR.

Thus ΔPQR is the required triangle.

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The below given steps will be followed to construct the required triangle.

Step I: Draw line segment QR of 6 cm. At point Q, draw an angle of 60°, say ∠XQR.

Step II: Cut a line segment QS of 2 cm from the line segment QT extended in the opposite side of line segment XQ. (As PR > PQ and PR − PQ = 2 cm). Join SR.

Step III: Draw perpendicular bisector AB of line segment SR. Let it intersect QX at point P. Join PQ, PR.

ΔPQR is the required triangle.

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