Chhattisgarh Board Solutions for Exercise 6: Exercise – 2

In the figure given below, $\mathrm{MN}\parallel \mathrm{ST}$, then find the value of $\frac{\mathrm{TN}}{\mathrm{RT}}$.

By using basic proportionality theorem, Prove that a line drawn through the midpoint of one side of a triangle parallel to another side bisects the remaining side?

In the figure given below, $\mathrm{DF}\parallel \mathrm{AE}$ and $\mathrm{DE}\parallel \mathrm{AC}$, then prove that, $\frac{\mathrm{BF}}{\mathrm{FE}}=\frac{\mathrm{BE}}{\mathrm{EC}}$.

In $△\mathrm{PQR}$, $\mathrm{E}$ and $\mathrm{F}$ are points on the sides $\mathrm{PQ}$ and $\mathrm{PR}$ respectively. Then for the given condition as  $\mathrm{PE}=3.9 \mathrm{cm}$, $\mathrm{EQ}=3 \mathrm{cm}$,  $\mathrm{PF}=3.6 \mathrm{cm}$, $\mathrm{FR}=2.4 \mathrm{cm}$, find out whether $\mathrm{EF}\parallel \mathrm{QR}$.

In $△\mathrm{PQR}$, $\mathrm{E}$ and $\mathrm{F}$ are points on the sides $\mathrm{PQ}$ and $\mathrm{PR}$ respectively. Then for the given condition as  $\mathrm{PE}=4 \mathrm{cm}$, $\mathrm{EQ}=4.5 \mathrm{cm}$,  $\mathrm{PF}=8 \mathrm{cm}$, $\mathrm{FR}=9 \mathrm{cm}$, find out whether $\mathrm{EF}\parallel \mathrm{QR}$.

In $△\mathrm{PQR}$, $\mathrm{E}$ and $\mathrm{F}$ are points on the sides $\mathrm{PQ}$ and $\mathrm{PR}$ respectively. Then for the given condition as$\mathrm{PQ}=1.28 \mathrm{cm}, \mathrm{PR}=2.56 \mathrm{cm}, \mathrm{PE}=0.18 \mathrm{cm}, \mathrm{PF}=0.36 \mathrm{cm}$, find out whether $\mathrm{EF}\parallel \mathrm{QR}$.

In the figure given below, $\mathrm{DE}\parallel \mathrm{OQ}$ and $\mathrm{DF}\parallel \mathrm{OR}$, show that $\mathrm{EF}\parallel \mathrm{QR}$,

In the figure given below, the points  $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ are located respectively on $\mathrm{OP}, \mathrm{OQ}$ and $\mathrm{OR}$ in such way that $\mathrm{AB}\parallel \mathrm{PQ}$ and $\mathrm{AC}\parallel \mathrm{PR}$. Show that $\mathrm{BC}\parallel \mathrm{QR}$.