Classifying Triangles by Sides and Angles

This page provides a comprehensive overview of triangle classification, focusing on both side lengths and angle measures. It serves as an excellent resource for students learning about the characteristics of different types of triangles.

Definition: A triangle is a three-sided polygon with three angles.

The page is divided into two main sections: classification by sides and classification by angles.

Classification by Sides:

1. Equilateral Triangle: All three sides are equal in length.
2. Isosceles Triangle: Two sides are equal in length.
3. Scalene Triangle: No two sides are equal in length.

Vocabulary: Equilateral means "equal sides," isosceles means "two equal sides," and scalene means "unequal sides."

Classification by Angles:

1. Acute Triangle: All angles are less than 90°.
2. Right Triangle: One angle is exactly 90°.
3. Obtuse Triangle: One angle is greater than 90°.

Highlight: A triangle can be classified by both its sides and angles simultaneously, leading to combinations like "acute isosceles" or "right scalene."

The page includes several examples of triangles, each labeled with their angle measures and side lengths. These examples demonstrate how to apply both side and angle classifications to real triangles.

Example: Triangle 7 has all angles measuring 60° and all sides equal to 8.6 units, making it an equilateral and equiangular (acute) triangle.

Other examples include:

• A right scalene triangle (90°, 32°, 58°; sides 11.2, 7, 13.2)
• An acute scalene triangle (79°, 57°, 44°; sides 6.1, 7.4, 8.7)
• An obtuse isosceles triangle (26°, 26°, 128°; sides 2.5, 2.5, 4.5)
• An acute isosceles triangle (72°, 72°, 36°; sides 3, 4.8, 4.8)
• A right isosceles triangle (90°, 45°, 45°; sides 4.8, 4.8, 6.8)

This comprehensive guide serves as an excellent classifying triangles worksheet, allowing students to practice identifying triangle types based on given measurements. It effectively covers the 7 types of triangles commonly studied in geometry: equilateral, isosceles, scalene, acute, right, obtuse, and their various combinations.