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Question

Construct a triangle PQR in which QR=6 cm,Q=60o and PRPQ=2 cm.

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Solution

1) Draw the base QR=6 cm.

At point Q draw a ray QX making an XQR=60.
Here, PRPQ=2 cm
PR>PQ
The side containing the base angle Q is less than third side.
2) Cut the line segment QS equal to PRPQ=2 cm, from the ray QX extended on opposite side of base QR.
3) Join SR and draw its perpendicular bisector ray LM which intersect SR at M.
4) Let P be the intersection point of SX and perpendicular bisector M. Then join PR.
Thus, PQR is the required triangle.



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