In abc if ab2=ac2+cb2 state with reason whether abc is a right angled triangle or not

The pictorial form of the given problem is as follows,

Pythagoras theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.

First, we consider the ΔABM and applying Pythagoras theorem we get,
AM2 = AB + BM2
AB2 = AM2 - BM2 ......(i)Now, we consider the ΔABC and applying Pythagoras theorem we get,

AC2 = AB2 + BC2

AB2 = AC2 - BC2 ......(ii)

From (i) and (ii) we get,
AM2 - BM2 = AC2 - BC2
AM2 + BC2 = AC2 + BM2
Hence Proved.

Yes it is a right angled triangle

statement:

Because if square of one side is equal to the sum of the squares of the other two sides. Then the angle opposite to the first side is right angle.It is a right angled triangle

For example,

In triangle ABC,

AB,AC,BC are sides of a triangle

so if AB2=AC2+BC2

Then the angle opposite to the side AC is called right angle.(From the statement mentioned above)

So it is a right angled triangle

Viktor

Jan 31, 2021