Practice set 3.4

In figure, point $A$ is on the bisector of $\angle XYZ.$ If $AX = 2 \mathrm{cm}$, then find $AZ$ (in $\mathrm{cm}$).

In figure, $\angle RST=56°$,$segPT\perp rayST,segPT\perp rayST,segPR\perp raySR and PR\cong seg PT$ Find the measure of $\angle RSP$ ( in degrees ). 

In $△PQR,PQ=10 \mathrm{cm},QR=12 \mathrm{cm},PR=8 \mathrm{cm}$. Find out the greatest and the smallest angle of the triangle.

In $△FAN, \angle F= 80°,\angle A=40°$. Find out the greatest and the smallest side of the triangle. State the reason.

Prove that an equilateral triangle is equiangular.

Prove that, if the bisector of $\angle BAC$ of $∆ABC$ is perpendicular to side $BC$, then $∆ABC$ is an isosceles triangle.

In figure, if $\mathrm{segment} \mathrm{PR}=\mathrm{segment} \mathrm{PQ}$, show that $\mathrm{segmenet} \mathrm{PS}>\mathrm{segment} \mathrm{PQ}$.

In $\Delta ABC$, segment $AD$ and segment $BE$ are altitudes and $AE=BD$. Prove that segment $AD\cong$ segment $BE$.