# 10. Construct $\triangle \mathrm{PQR}$ with $\mathrm{PQ}=4.5 \mathrm{~cm}, \angle \mathrm{P}=60^{\circ}$ and $\mathrm{PR}=4.5 \mathrm{~cm} .$ Measure $\angle \mathrm{Q}$ and $\angle \mathrm{R}$. What type of a triangle is it?

Given: $PQ=4.5\ cm,\ \angle P=60^{o}$ and $PR=4.5\ cm$.

To do: To construct $\vartriangle PQR$ and and Measure $\angle Q$ and $\angle R$. And to find the type of this triangle.

Solution:

1. Draw a line $PQ=4.5\ cm$, with the help of scale.

2. With the help of proctor , Draw $\angle XPQ=60^{o}$.

3. Measure compass to $4.5\ cm$  and mark on $XP$ at point $R$, while $P$ is the center.

4.  Join $QR$.

$\vartriangle PQR$, is the required triangle.

With the help of proctor, when we measure $Q$ and $R$. We find it $60^{o}$ both.

And when we measure $QR$, it is $4.5\ cm$.

Here we found that $\angle P=\angle Q=\angle R=60^{o}$ and $PQ=QR=RP=4.5\ cm$.

All its sides and angles are equal.

Hence, It is an equilateral Triangle.

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Updated on: 10-Oct-2022

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