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Question

Construct $$\Delta PEN$$ with $$PE=4\ cm,\ EN=5\ cm$$ and $$NP=3\ cm$$. 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?


Solution

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.

Mathematics

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