Question

In triangle ABC, $B{C}^2$ + $A{B}^2$ = $A{C}^2$, then __________ is a right angle

• A. $\angle A$
• B. $\angle B$
• C. $\angle C$
• D. None

Answer 1

The correct option is B $\angle B$

In $△ABC,$

$\Rightarrow$ $(AC{)}^2=(BC{)}^2+(AB{)}^2$ [ Given ] --- ( 1 )

Pythagoras theorem,

$\Rightarrow$ $(Hypotenuse{)}^2=(oneside{)}^2+(otherside{)}^2$ ---- ( 2 )

Comparing ( 1 ) and ( 2 ) we get, $AC$ is a hypotenuse of a triangle.

$\Rightarrow$ Hypotenuse is the longest side of a right-angled triangle, opposite the right angle.

$\Rightarrow$ Opposite angle of $AC$ is $\angle B.$

$\therefore$ $\angle B$ is a right angle of $△ABC.$