What characterizes a right triangle?

What characterizes a right triangle?

• A. A triangle that has all sides unequal
• B. A triangle that has two equal sides
• C. A triangle that has a 90-degree angle
• D. A triangle that has one angle greater than 90 degrees

Answer: (C)

A right triangle is specifically characterized by having one angle that measures exactly 90 degrees. This right angle distinguishes it from other types of triangles, such as acute triangles, which have all angles less than 90 degrees, and obtuse triangles, which possess one angle greater than 90 degrees. The presence of the right angle allows for the application of the Pythagorean theorem, which relates the lengths of the sides of the triangle, and sets the foundation for various calculations and principles in geometry. A right triangle can have various side lengths, being classified further into isosceles (having two equal sides) or scalene (with all sides of different lengths), but the defining feature remains the right angle. Thus, the correct answer captures the essential property that makes a right triangle unique among all other triangle types.

A right triangle is specifically characterized by having one angle that measures exactly 90 degrees. This right angle distinguishes it from other types of triangles, such as acute triangles, which have all angles less than 90 degrees, and obtuse triangles, which possess one angle greater than 90 degrees.

The presence of the right angle allows for the application of the Pythagorean theorem, which relates the lengths of the sides of the triangle, and sets the foundation for various calculations and principles in geometry. A right triangle can have various side lengths, being classified further into isosceles (having two equal sides) or scalene (with all sides of different lengths), but the defining feature remains the right angle. Thus, the correct answer captures the essential property that makes a right triangle unique among all other triangle types.