$P$ is a point in the exterior of $∆XYZ$ as shown in the figure. $PX,PY$ and $PZ$ are joined.

Is $2(PX+PY+PZ)>(XY+YZ+ZX)$? How?

 

The angles of a triangle are in the ratio $2:3:4$. Find the measure of all the angles of the triangle.

$AT,EM \text{and} PI$ are the medians of $∆APE$ as shown in the figure. If $AP=8 \mathrm{cm}, AE=7 \mathrm{cm} \text{and} PE=6.4 \mathrm{cm}$, then find the length of $AM,MP,PT,TE,EI \text{and} IA$.

In $∆MTR$, if $MT=TR$, then $\angle R=\angle$_____

In $∆PHD$, if $\angle P=\angle D$, then $PH=$_____

In $∆RAW$, if $\angle ARW=\angle WAR$, then $AW=$_____

In $∆TEA$, if $ET=AT$, then $\angle A=\angle$_____

In $∆PQR$, if $PQ=QR$, then $\angle P=\angle$_____

Two sides of an isosceles triangle are $4 \mathrm{cm} \text{and} 9 \mathrm{cm}$, respectively. Which of the following will be the measure of the third side?