Question

Construct $△\mathrm{PQR}$ in which $\mathrm{PQ}=5.2\mathrm{cm}$, $\mathrm{QR}=5.2\mathrm{cm}$, and $\angle \mathrm{Q}=30°$. Measure $\angle \mathrm{R}$. What type of triangle, according to sides, is this ?

Answer 1

Step 1: Draw a line segment $\mathrm{PQ}=5.2\mathrm{cm}$

Step 2: From the point Q draw a line QD making an angle of $30°$

Step 3: With Q as center and radius $5.2\mathrm{cm}$, draw an arc cutting QD at R

Step 4: Join PR

Since, side $\mathrm{PQ}=\mathrm{RQ}$,

By measurement, we get $\angle P=\angle R=75°$ [Measuring by protractor]

If in any triangle two sides and their corresponding angles are equal then this type of triangle is called an isosceles triangle.

Hence, $△\mathrm{PQR}$ is an isosceles triangle $\mathrm{PQ}=\mathrm{RQ},\mathrm{and}\angle R=75$.