$P$ is any point inside the triangle $ABC$. Prove that: $\angle BPC>\angle BAC$.

In the following diagram; $AD = AB$ and $AE$ bisects angle $A$. Prove that :

$BE = DE$

In the following diagram; $AD = AB$ and $AE$ bisects angle $A$. Prove that :

$\angle ABD>\angle C$

In the following figure; $AB$ is the largest side and $BC$ is the smallest side of triangle $ABC$.

Write the angles $xº, yº \text{and} zº$ in ascending order of their values.

In quadrilateral $ABCD$, side $AB$ is the longest and side $DC$ is the shortest. Prove that :

$\angle D > \angle B$

In triangle $ABC$, side $AC$ is greater than side $AB$. If the internal bisector of angle $A$ meets the opposite side at point $D$, prove that: $\angle ADC$ is greater than $\angle ADB$.