Maharashtra Board Solutions for Chapter: Similarity, Exercise 2: Practice set 1.2

In $\Delta \mathrm{MNP}, \mathrm{NQ}$  is a bisector of $\angle \mathrm{N}$. If  $\mathrm{MN}=5, \mathrm{PN}=7, \mathrm{MQ}=2.5$, then find $\mathrm{QP}$.

In trapezium $ABCD,$ side $\mathrm{AB}\Vert$ side $\mathrm{PQ}\Vert$ side $\mathrm{DC}, \mathrm{AP}=15, \mathrm{PD}=12, \mathrm{QC}=14$, find $\mathrm{BQ}$.

Find $\mathrm{QP}$ using given information in the figure.

In below figure if $\mathrm{AB}\Vert \mathrm{CD}\Vert \mathrm{FE}$, then find $x$  and $\mathrm{AE}$

In $\Delta \mathrm{LMN}$, ray MT bisects $\angle \mathrm{LMN}$. If $\mathrm{LM}=6, \mathrm{MN}=10, \mathrm{TN}=8$, then find $\mathrm{LT}.$

In $\Delta \mathrm{ABC},$ seg $\mathrm{BD}$ bisects $\angle \mathrm{ABC}$. If $\mathrm{AB}=\mathrm{x}, \mathrm{BC}=\mathrm{x}+5, \mathrm{AD}=\mathrm{x}-2, \mathrm{DC}=\mathrm{x}+2$, then find the value of $x$.

In the figure, $X$ is any point in the interior of triangle. Point $X$  is joined to vertices of triangle. Seg $\mathrm{PQ}\Vert seg\mathrm{DE},seg\mathrm{QR}\Vert seg\mathrm{EF}$. Prove that Seg $\mathrm{PR}\Vert seg\mathrm{DF}$ 

In $△\mathrm{ABC},$ ray $\mathrm{BD}$ bisects $\angle \mathrm{ABC}$ and ray $\mathrm{CE}$ bisects $\angle \mathrm{ACB}.$ If $\mathrm{seg} \mathrm{AB}\cong \mathrm{seg} \mathrm{AC}$ then prove that $\mathrm{ED}\parallel \mathrm{BC}$.