Honors Geometry Companion Book, Volume 1

4.1.1 Classifying Triangles

Key Objectives • Classify triangles by their angle measures and side lengths. • Use triangle classifications to find angle measures and side lengths. Key Terms • An acute triangle has three acute angles. • An equiangular triangle has three congruent angles. • A right triangle has one right angle. • An obtuse triangle has one obtuse angle. • An equilateral triangle has three congruent sides. • An isosceles triangle has at least two congruent sides. • A scalene triangle has no congruent sides.

A triangle is a closed plane figure with three sides and three vertices. Each of a triangle’s sides is a line segment and each vertex is the endpoint of two of these segments. Since a triangle always has three sides and three vertices, a triangle also has three interior angles. All triangles can be classified by the measure of its interior angles or by the lengths of its sides. Example 1 Classifying Triangles by Angle Measures A triangle can be classified by its angle measures. When a triangle is classified by its angle measures, there are four possibilities: acute (all angles are acute), equiangular (all angles are congruent), right (one right angle), and obtuse (one obtuse angle).


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