Question

State whether the following statement is true or false.

ABC is a Triangle in which AB=AC. If the bisectors of $\angle Cand\angle B$ meet AC & AB in D & E Respectively. then the BD=2CE.

• A. True
• B. False

Answer 1

The correct option is B False

Given $AB=AC[\angle B=\angle C]$ and bisector of $\angle B$ and $\angle C$ meet $AC$ and $AB$ at $D$ and $E$ respectively.

Now, in $\Delta BCD$ and $\Delta CBE$:

$\angle B=\angle C$.......[given $AB=AC$]

$BC=BC$.....[common]

$\angle CBD=\angle BCE$.......[half of the angle $B$=half of angle $C$]

Hence, $\Delta BCD\cong \Delta CBE$.....[By $ASA$ condition]

So, $BD=CE$......[by $CPCT$]