Question

answer the following questions.

1. choose the correct answer.

the converse of the pythagorean theorem states that if the sum of the squares of the lengths of two sides of a triangle is equal to the square of the measure of its third side, then the triangle is a(n) ____ triangle.
options: equilateral, acute, obtuse, right

Explanation:

The Converse of the Pythagorean Theorem is a fundamental concept in Geometry (a subfield of Mathematics). It states that if \(a^2 + b^2 = c^2\) (where \(a\), \(b\), and \(c\) are the side lengths of a triangle, with \(c\) being the longest side), then the triangle is a right triangle. An equilateral triangle has all sides equal, an acute triangle has all angles less than \(90^\circ\), and an obtuse triangle has one angle greater than \(90^\circ\). None of these match the converse's conclusion except a right triangle.

Answer:

D. right