Question

Classify each triangle by its angles (acute, right, obtuse, equiangular) and its sides (scalene, isosceles, or equilateral). a) Acute and scalene b) Right and isosceles c) Obtuse and equilateral d) Equiangular and scalene

Answer 1

Triangles can be classified by their angles (acute, right, obtuse, equiangular) and their sides (scalene, isosceles, equilateral). However, some combinations such as obtuse equilateral and scalene equiangular do not exist due to contradicting properties.

Step-by-step explanation:

We classify triangles in two ways: by their angles and by their sides. These classifications help us understand and define the properties of the triangle.

• An acute triangle has all angles less than 90° and a scalene triangle has all sides of different length. Hence, an acute-scalene triangle would all angles less than 90° and each side would be of different length.
• A right triangle contains one 90° angle and an isosceles triangle has at least two sides of equal length. Therefore, a right-isosceles triangle would have one 90° angle and two sides of the same length.
• An obtuse triangle has one angle greater than 90° and an equilateral triangle has all sides of equal length. However, an obtuse and equilateral classification cannot exist together in a triangle as all angles in an equilateral triangle are 60° which conflicts with the obtuse requirement.
• An equiangular triangle has all angles equal and if it was also to be scalene, it would contradict itself as an equiangular triangle has to have all sides of equal length aka equilateral. Therefore, a scalene-equiangular triangle does not exist.

Learn more about Triangle Classification