Question

Which statement can be approved through using the given theorem?

A. The sum of the angles in a triangle is always 180 degrees.
B. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
C. Two parallel lines are cut by a transversal; the alternate interior angles are equal.
D. The area of a circle is given by the formula A=πr2.

Answer 1

Statement B is correct according to the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is the sum of the squares of the other two sides. The theorem is represented by the equation a² + b² = c² and is fundamental in calculating distances in geometry.

Step-by-step explanation:

The correct statement that can be approved using the given theorem is B. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. According to the Pythagorean theorem, in any right-angled triangle, the relationship between the lengths of the sides is defined by the equation a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.

This relation can be rewritten to solve for the hypotenuse, resulting in c = √a² + b². This helps in calculating the straight-line distance between two points when forming a right triangle, substantiating the old adage that the shortest distance between two points is a straight line.