Question

Construct $\Delta PEN$ with $PE=4cm,EN=5cm$ and $NP=3cm$. If you draw circle instead of arcs how many points of intersection do you get ? How many triangles with given measurements are possible ? Is this true in case of every triangle?

Answer 1

1. Draw line $PE=4$cm using scale

2. At point $P$ , taking $P$ as center draw arc of radius $3$cm

3. Draw a arc of radius $5$cm taking $E$ as center.Let both arc intersect at point $N$.

4. Join line $EN$ and $NP$ using scale .

5. If the circles are drawn they will intersect at another point below line $PE$.You will get congruent triangle. This is true for all triangles.