Question

In AABC, if AC2 = ABP + BC then the triangle is right angled at
which vertex ?​

Answer 1

Answer: The triangle is right - angled at the vertex 'B'.

Step-by-step explanation:

Given: We are given a triangle ΔABC in which AC² = AB² + BC².

What to do? We need to check at which vertex, the triangle is right angled.

Solution:

Pythagoras Theorem states that, in a right angled triangle, the square of hypotenuse is equal to the sum of square of other two sides of the triangle.

→ Hypotenuse² = Perpendicular² + Base²

Where,

• Hypotenuse = AC
• Perpendicular = AB
• Base = BC

We know that, the side opposite to hypotenuse is known as the perpendicular side.

If you refer the attached figure, side opposite to AC is AB, which is the perpendicular side of ΔABC.

Since AB is perpendicular, ∠B = 90°.

Final Answer: Therefore, the triangle is right angled at the vertex, 'B'.