Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.

Verified step by step guidance

1. Identify the measures of the three angles of the triangle. This is essential because the classification into acute, right, or obtuse depends on the angles.
2. Classify the triangle by its angles: if all angles are less than 90°, it is acute; if one angle is exactly 90°, it is right; if one angle is greater than 90°, it is obtuse.
3. Next, determine the lengths of the three sides of the triangle. This will help classify the triangle as equilateral, isosceles, or scalene.
4. Classify the triangle by its sides: if all three sides are equal, it is equilateral; if exactly two sides are equal, it is isosceles; if all sides are different lengths, it is scalene.
5. Combine both classifications to fully describe the triangle, for example, an acute isosceles triangle or a right scalene triangle.

Key Concepts

Classification of Triangles by Angles

Triangles are classified based on their angles into acute (all angles less than 90°), right (one angle exactly 90°), or obtuse (one angle greater than 90°). Understanding these categories helps determine the triangle's shape and properties.

Classification of Triangles by Sides

Triangles are also classified by side lengths as equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides different). This classification provides insight into the triangle's symmetry and side relationships.

Using Angle Measures and Side Lengths to Classify Triangles

To classify a triangle fully, one must analyze both its angles and side lengths. This often involves calculating or measuring angles and sides, then applying the definitions of angle-based and side-based classifications to identify the triangle type.