Manipur Board Solutions for Chapter: Triangles, Exercise 3: EXERCISE 7.3

$AD$ is a median of $△ABC$. The bisector of $\angle ADB$ and $\angle ADC$  meet $AB$ and $AC$ at $E$ and $F$ respectively. Prove that $EF\parallel BC$.

If the bisector of an angle of a triangle bisects the opposite sides, prove that the triangle is isosceles.

In $△ABC$, the bisector of $\angle B$ meets $AC$ at $D$. A line $PQ$ is drawn parallel to $AC$ meeting $AB, BC$ and $BD$ at $P, Q$ and $R$ respectively. Show that $PR\times BQ=\times QR\times BP$ 

 In $△ABC$, the bisector of $\angle B$ meets $AC$ at $D$. A line $PQ$ is drawn parallel to $AC$ meeting $AB, BC$ and $BD$ at $P, Q$ and $R$ respectively. Show that $AB\times CQ=BC\times AP$ 

If the median of a triangle are bisectors of the corresponding angles of the triangle, prove that the triangle ie equilateral.

The bisectors of the $\angle B$ and $\angle C$ of a triangle $ABC$ meet the opposite sides at $D$ and $E$ respectively. If $ED\parallel BC$, prove that the triangle is isosceles.