Question

In the isosceles right angled triangle $△ABC$ right angled at $B$, the perpendicular is drawn to the hypotaneus which meet hypotaneus at $D$.
Choose the correct option.

• A. $△ABD\cong △CBD$
• B. $D$ bisects side $AC$
• C. Both $\left(a\right)$ and $\left(b\right)$ correct
• D. None correct

Answer 1

The correct option is C Both $\left(a\right)$ and $\left(b\right)$ correct


In $△ABD$ and $△CBD$

$BD=BD$ (common side in both)

$\angle ADB=\angle CDB={90}^o$

$AB=CB$ (isosceles triangle)

So, $△ABD\cong △CBD$ (Hypotenuse Leg Congruency)

So, $AD=CD$ (Corresponding sides of congruent triangles are equal)

Hence, $D$ bisects $AC$.
So, option $\left(c\right)$ correct.