Question

In triangle ABC, where angle C = 90 degrees and triangle ABC is isosceles, which of the following options proves that AB^2 = AC^2?

Answer 1

In an isosceles triangle ABC with a right angle at C, AB^2 = AC^2 can be proved using the Pythagorean theorem.

Step-by-step explanation:

In an isosceles triangle ABC with a right angle at C, we can prove that AB^2 = AC^2 using the Pythagorean theorem. The square of the hypotenuse, or side opposite the right angle, in a right triangle is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem.

We may determine that AB = AC since triangle ABC is isosceles. Let's denote the length of AB as a and the length of BC as b. The Pythagorean theorem can be written as a^2 + b^2 = c^2, where c represents the hypotenuse. Since triangle ABC is isosceles, we have a^2 + b^2 = AC^2.

Since angle C is a right angle, we can use the given information to determine the equation. Therefore, AB^2 = AC^2.