Question 23

A triangle has angles of 90 degrees, 45 degrees and 45 degrees. Select all the names that correctly describe this triangle.

Right-angled, because one angle is exactly 90 degrees.Correct answer
Isosceles, because two angles match and so do two sides.Correct answer
Equilateral, because a right angle counts as a third equal angle.
Scalene, because its three angles are not all the same.

Explanation

The 90 degree angle settles the angle axis, while the pair of 45 degree angles forces the two sides facing them to match, which settles the side axis as well, so two names apply together. Denying any equal sides here contradicts the equal angles, because matching angles always face matching sides.

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Question 23: A triangle has angles of 90 degrees, 45 degrees and 45… · Geometry Basics · Questena