Maharashtra Board Solutions for Chapter: Triangles, Exercise 6: Problem set 3

If two sides of a triangle are $5 \mathrm{cm}$ and $1.5 \mathrm{cm}$, the length of its third side cannot be

In $\Delta PQR$, if $\angle R>\angle Q$ then

In $\Delta TPQ,\angle T = {65}^0,\angle P = {95}^0$, which is a true statement?

In $\Delta PQR$, if $PQ>PR$ and bisectors of $\angle Q$ and$\angle R$ intersects at $S$. Shows that $SQ>SR.$

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 $PQ+QR+RP>2PS$.

In figure, bisector of $\angle BAC$ intersects side $BC$ at point $D$. Prove that $AB>BD$.

In figure, segment $AD\perp$segment $BC$. Segment $AE$ is the bisector of $\angle CAB$ and $C-E-D$. Prove that $\angle DAE=\frac{1}{2}(\angle B-\angle C)$.