Question

In any right angled triangle perpendicular bisectors meet the mid point of the triangle. State True/False.

• A. True
• B. False

Answer 1

The correct option is A True


Let M be the mid-point of AC; draw a perpendicular to DC passing through M and it intersects DC at N.
$⟹AM=MC$
$⟹AC=2MC$

The two trianles ABC and MNC are similar. (AAA property)

$⟹\frac{AC}{MC}=\frac{BC}{NC}$
$⟹\frac{2MC}{MC}=\frac{BC}{NC}$
$⟹BC=2NC$

Therefore N is the midpoint of BC. So, line MN is the perpendicular bisector of BC.
Similarly, It can be proved for other sides.

In any right angled triangle perpendicular bisectors meet the mid point of the triangle.