Question

Which one is not correct with right triangle ABC with angle (B = 90) degrees?

a) (AB² + BC² = AC²)

b) (AB² + AC² = BC²)

c) AC is the hypotenuse

d) Angle (A +) Angle (C =) Angle (B)

Answer 1

In a right triangle ABC with angle B = 90 degrees, the correct representation of the Pythagorean theorem is (AB² + BC² = AC²), making option b) (AB² + AC² = BC²) not correct.

Step-by-step explanation:

In a right triangle ABC with angle B = 90 degrees, the Pythagorean theorem can be used to relate the lengths of the legs (AB and BC) to the length of the hypotenuse (AC).

The correct representation of the theorem is a) (AB² + BC² = AC²), which states that the sum of the squares of the legs equals the square of the hypotenuse. Therefore, the option b) (AB² + AC² = BC²) is not correct.

To further illustrate this, let's consider an example:

If AB = 3 units and BC = 4 units, according to the Pythagorean theorem, AC² = AB² + BC² = 3² + 4² = 9 + 16 = 25. Taking the square root of both sides, we find AC = 5 units.

Therefore, option b) is not correct with right triangle ABC.