Question

Question 7
D is any point on side AC of a $\Delta ABC$ with AB = AC. Show that CD < BD.

Answer 1

Given: In $\Delta ABC$, AB = AC and D is any point of side AC.


In $\Delta ABC$ AC = AB [given]
$\Rightarrow \angle ABC=\angle ACB...\left(i\right)$
[angles opposite to equal sides are equal]

In $\Delta ABC,\angle ABC>\angle DBC$ [since, $\angle DBC$ is a part of $\angle B]$
$\Rightarrow \angle ACB>\angle DBC$ [From Eq.(i)]
$\Rightarrow BD>CDorCD<BD$ [side opposite to greater angle is longer]