Question

in angle ABC if AB2=AC2+CB2 state with reason wheter angle ABC is a right angled triangled or not​

Answer 1

Answer:

Given:

\textsf{In triangle ABC,}In triangle ABC,

\mathsf{AB^2=AC^2+BC^2}AB

2

=AC

2

+BC

2

\underline{\textsf{To find:}}

To find:

\textsf{Whether triangle ABC is right angled or not}Whether triangle ABC is right angled or not

\underline{\textsf{Solution:}}

Solution:

\underline{\textsf{Converse of Pythagoras theorem:}}

Converse of Pythagoras theorem:

\textsf{If square of one side of a triangle is equal to sum of the}If square of one side of a triangle is equal to sum of the

\textsf{squares of the other two sides, then the angle contained}squares of the other two sides, then the angle contained

\textsf{by the two sides is right angle.}by the two sides is right angle.

\textsf{Consider,}Consider,

\mathsf{AB^2=AC^2+BC^2}AB

2

=AC

2

+BC

2

\textsf{According to converse of Pythagoras theorem,}According to converse of Pythagoras theorem,

\mathsf{{\triangle}ABC}\;\textsf{is right angled}△ABCis right angled

Answer 2

Given data,

In a triangle $ABC$,

if $AB^{2} =AC^{2} +CB^{2}$

We have to check whether the triangle is right angled triangle or not.

By Pythagorean theorem,

Square of Hypotenuse is equal to sum of squares of other two sides

In triangle $ABC$,

$AC$ will be the hypotenuse.

According to the statement of Pythagorean theorem, from the given equation $AB$ will be the hypotenuse.

If $AC$ is the hypotenuse, the statement might be true.

Therefore, the given statement is false, the triangle is not a right angled triangle.