Question

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: obtuse, equilateral, acute, 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 \( a \), \( b \) are the lengths of two sides and \( c \) is the length of the third side of a triangle), then the triangle is a right triangle. An obtuse triangle would have \( a^2 + b^2 < c^2 \) (for the longest side \( c \)), an equilateral triangle has all sides equal (not related to this theorem's condition), and an acute triangle would have \( a^2 + b^2 > c^2 \) (for the longest side \( c \)). So the correct answer is based on the definition of the converse of the Pythagorean Theorem.

Answer:

D. right