If $\Delta ABC \cong \Delta RPQ$ and the perimeter of $\Delta ABC$ is $18 \, cm$,then the perimeter of $\Delta PQR$ is $cm$.

In the figure,$AC = AE$,$AB = AD$ and $\angle BAD = \angle EAC$. Show that $BC = DE$.

$AB$ is a line segment and line $l$ is its perpendicular bisector. If a point $P$ lies on $l$,show that $P$ is equidistant from $A$ and $B$.

$\Delta ABC$ and $\Delta DBC$ are two isosceles triangles on the same base $BC$ and vertices $A$ and $D$ are on the same side of $BC$ (see Fig). If $AD$ is extended to intersect $BC$ at $P$,show that:
$(i)$ $\Delta ABD \cong \Delta ACD$
$(ii)$ $\Delta ABP \cong \Delta ACP$
$(iii)$ $AP$ bisects $\angle A$ as well as $\angle D$.
$(iv)$ $AP$ is the perpendicular bisector of $BC$.

It is given that $\triangle ABC \cong \triangle FDE$. If $AB = 5 \, cm$,$\angle B = 40^{\circ}$,and $\angle A = 80^{\circ}$,then which of the following is true?

Complete the hexagonal and star-shaped Rangolies [see Fig. $(i)$ and $(ii)$] by filling them with as many equilateral triangles of side $1\,cm$ as you can. Count the number of triangles in each case. Which has more triangles?