Which statement about a scalene triangle is true?

Which statement about a scalene triangle is true?

• A. All sides equal.
• B. Two sides equal.
• C. All sides and all angles different.
• D. One angle 90 degrees.

Answer: (C)

A scalene triangle has all sides with different lengths, and that forces all three interior angles to be different as well. If two angles were equal, the sides opposite them would be equal, which would contradict scalene. So the defining picture is: every side is different and every angle is different. The other statements describe other triangle types or possibilities that aren’t required by scalene. For example, all sides equal would be an equilateral triangle, two sides equal would be isosceles, and having a right angle describes a right triangle but isn’t what makes a triangle scalene.

A scalene triangle has all sides with different lengths, and that forces all three interior angles to be different as well. If two angles were equal, the sides opposite them would be equal, which would contradict scalene. So the defining picture is: every side is different and every angle is different.

The other statements describe other triangle types or possibilities that aren’t required by scalene. For example, all sides equal would be an equilateral triangle, two sides equal would be isosceles, and having a right angle describes a right triangle but isn’t what makes a triangle scalene.