# Construct a

Here, we are supposed to construct an isosceles triangle PQR, with base PQ and altitude from R on PQ given.

Steps of construction will be:

1. Draw a line segment sufficiently long using a ruler.

2. Locate points P and Q on the line such that PQ = 7.2 cm on the previously drawn line segment using a ruler.

3. Draw a perpendicular bisector of PQ.

For this, fix your compass at approximately more than the length of PQ and make a circle or semicircle, or two arcs taking P as centre on either sides of the line segment PQ, then similarly make two more arcs taking Q as centre cutting the previous arcs. Join the two intersections and call it MX with M on PQ.

4. With M as centre and radius 5 cm, draw an arc cutting MX at R using a compass.

5. Join PR and QR.

Thus, PQR is the required triangle.

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