R K Bansal Solutions for Exercise 1: EXERCISE

Sides $AB \text{and} AC$ of a triangle $ABC$ are equal. $BC$ is produced through $C$ up to point $D$ such that $AC = CD$. $D$ and $A$ are joined and produced (through vertex $A$) up to point $E$. If angle $BAE=108°$; find angle $ADB$.

The given figure shows an equilateral triangle $ABC$ with each side $15 \mathrm{cm}$. Also $DE\parallel BC, DF\parallel AC$ and $EG\parallel AB$. If

If all the three altitudes of a triangle are equal, the triangle is equilateral. Prove it.

In $△ABC$, the internal bisector of angle $A$ meets opposite side $BC$ at point $D$. Through vertex $C$, line $CE$ is drawn parallel to $DA$ which meets $BA$ produced at point $E$. Show that $△ACE$ is isosceles.

In triangle $ABC$, bisector of angle $BAC$ meets opposite side $BC$ at point $D$. If $BD = CD$, prove that $△ABC$ is isosceles.

In $△ABC, D$ is a point on BC, such that $AB=AD=BD=DC$. Show that $\angle ADC : \angle C = 4 : 1.$

Using the information, given in each of the following figures, find the values of $a \text{and} b$.

$\left[\text{Given}: CE=AC\right]$

Using the information, given in each of the following figures, find the values of a and b.