Question

classify this triangle by its sides.
scalene
equilateral
isosceles but not equilateral

Explanation:

Step1: Recall triangle side classifications

A scalene triangle has all sides of different lengths (and all angles different). An equilateral triangle has all three sides equal (and all angles \(60^\circ\)). An isosceles triangle has at least two sides equal (and at least two angles equal). If a triangle is isosceles but not equilateral, it has exactly two equal sides (and two equal angles, one different).

Step2: Analyze the given triangle

The triangle has two equal - looking angles (the base angles) and one different angle (the vertex angle). By the isosceles triangle theorem (if two angles of a triangle are equal, then the sides opposite those angles are equal), this triangle has two equal sides. Since it doesn't have all three angles equal (so not all three sides equal), it is isosceles but not equilateral. It is not scalene (since scalene has all sides different, meaning all angles different) and not equilateral (since equilateral has all angles equal).

Answer:

isosceles but not equilateral