Question

classify the triangle by its sides and by measuring its angles.
the triangle can be classified by its angles as
and by its sides as
scalene right equilateral obtuse equiangular
isosceles acute

Explanation:

Step1: Analyze by sides

A triangle with all three sides equal (marked with tick marks on all sides) is an equilateral triangle. Also, an equilateral triangle is a special case of isosceles (but equilateral is more specific here). So by sides, it's equilateral (or also isosceles, but equilateral is the most accurate as all sides are equal).

Step2: Analyze by angles

An equilateral triangle has all angles equal to \(60^\circ\), which are all acute (less than \(90^\circ\)) and also equiangular (all angles equal). So by angles, it can be classified as acute (or equiangular, but acute is about angle measure being less than \(90^\circ\), and equiangular is about all angles equal; since all \(60^\circ\) angles are acute, and also equiangular).

Answer:

By angles: acute (or equiangular); By sides: equilateral (or isosceles)

(Note: The most precise for sides is equilateral (since all three sides are marked equal), and for angles, since all angles are \(60^\circ\) (acute) and equal (equiangular), but the options include acute and equiangular, and for sides equilateral and isosceles. The triangle in the diagram has all three sides marked with the same tick, so it's equilateral by sides. By angles, since all angles are acute (less than \(90^\circ\)) and equal (equiangular), but the options have acute and equiangular. So the answers are:

By angles: acute (or equiangular); By sides: equilateral (or isosceles, but equilateral is more accurate here as all three sides are equal))