Prove that an equilateral triangle is equiangular.

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 $BE$.

If$\Delta XYZ ~ \Delta LMN$write the corresponding angles of the two triangles and also write the ratios of corresponding sides.

In $\Delta XYZ$, $XY=$$4 \mathrm{cm}$, $YZ=$$6 \mathrm{cm}$, $XZ=$$5 \mathrm{cm}$, if $\Delta XYZ ~ \Delta PQR$ and $PQ=8 \mathrm{cm}$, then find the lengths of remaining sides of $\Delta PQR.$

Draw a sketch of a pair of similar triangles. Label them. Show their corresponding angles by the same signs. Show the lengths of corresponding sides by numbers in proportion.

$∆ABC$ is isosceles in which $AB=AC$. Segment $BD$ and segment $CE$ are medians. Show that $BD=CE$.

In figure, point $D$ and $E$ are on side $BC$ of$\Delta ABD,$ such that $BD=CE$ and $AD=AE.$ Show that $\Delta ABD \cong \Delta ACE.$

In figure, $S$ is any point on side $∆PQR$. Prove that $PQ+QR+RP>2PS$.