Question

The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

• A. True
• B. False

Answer 1

The correct option is A True

Consider an isosceles triangle ABC, with AB = AC. BD and CE are median on AC and AB respectively.
Now, $AB=AC$
$\frac{1}{2}AB=\frac{1}{2}AC$
$BE=CD$ (I)
Now, In $△BDC$ and $△CEB$
$\angle DBC=\angle ECB$ (Isosceles triangle property)
$BC=BC$ (Common)
$BE=CD$ (From I)
$△BDC\cong △CEB$ (SAS postulate)
or $BD=CE$ (By cpct)
Hence, the medians corresponding to equal sides of an isosceles triangle are equal