O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 3: Exercise

In the figure, $AB<BC$. If the base angles of $△ABC$ are $70°$ and $50°$, state which of the two is $70°$.  $AM$ bisects the exterior angle $BAX$ and $AP$ is parallel to $CB$. Find $\angle MAP$.

In the given figure, if $\angle 1=\angle 2$, prove that $BA>BD$.

In the figure given below, $ABC$ is a triangle in which $AC>AB$ and the bisectors of angles $B$ and $C$ intersect each other at $O$. Prove that $OC>OB$.

In the figure given below, $AB=AC$, then prove that $CD>BD$.

Diagonal $PR$ and $QS$ of a quadrilateral $PQRS$ intersect each other at $O$. Prove that $PQ+QR+RS+SP>PR+QS$.

Diagonal $PR$ and $QS$ of a quadrilateral $PQRS$ intersect each other at $O$. Prove that $PQ+QR+RS+SP<2(PR+QS)$.

Prove that any two sides of a triangle are together greater than the third side.

Prove that in a triangle the difference of any two sides is less than the third.