Prakash Tiwari and Ishita Joshi Solutions for Chapter: Triangle and Its Properties, Exercise 5: Let's Practice

Prove that each angle of an equilateral triangle is $60°$.

In the adjoining figure, find the values of the exterior angle formed at the vertices of $∆PQR$.

$∆\mathrm{LMN}$ is an isosceles triangle with $\angle M=\angle \mathrm{N}$ and $\angle \mathrm{L}=80°$. If the bisectors of $\angle M$ and $\angle N$ meet at $\mathrm{O}$, then find the measures of all the angles of $∆MNO$.

Between which two numbers can the length of the third side of a triangle fall if the lengths of two sides are $7 \mathrm{cm}$ and $10 \mathrm{cm}$.

In the quadrilateral $PQRS$, if the diagonals $PR$ and $QS$ intersect at $O$, then prove that $PQ+QR+RS+PS>2QS$.

In the quadrilateral $PQRS$, if the diagonals $PR$ and $QS$ intersect at $O$, then prove that $PQ+QR+RS+PS>2PR$.

In the quadrilateral $PQRS$, if the diagonals $PR$ and $QS$ intersect at $O$, then prove that $2(PR+QS)>PQ+QR+RS+PS$.

A wire of length $18 \mathrm{cm}$ is bent to form an isosceles triangle of integral sides. Give the measures of sides of three possible isosceles triangles that can be bent with the wire.