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

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Step 1: Review the definitions of triangle types. An acute triangle has all angles less than 90 degrees, a right triangle has one angle exactly 90 degrees, and an obtuse triangle has one angle greater than 90 degrees.

Step 2: Review the definitions of triangle classifications based on side lengths. An equilateral triangle has all sides equal, an isosceles triangle has at least two sides equal, and a scalene triangle has all sides of different lengths.

Step 3: Examine the given triangle's angles to determine if it is acute, right, or obtuse. Use the angle measures provided or calculate them if necessary.

Step 4: Examine the given triangle's side lengths to determine if it is equilateral, isosceles, or scalene. Use the side lengths provided or calculate them if necessary.

Step 5: Combine the classifications from steps 3 and 4 to fully classify the triangle by both its angles and its side lengths.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Types of Angles

Triangles can be classified based on their angles into three types: acute, right, and obtuse. An acute triangle has all angles less than 90 degrees, a right triangle has one angle exactly equal to 90 degrees, and an obtuse triangle has one angle greater than 90 degrees. Understanding these classifications is essential for determining the type of triangle based on its angle measures.

Types of Triangles by Sides

Triangles can also be classified based on the lengths of their sides into equilateral, isosceles, and scalene. An equilateral triangle has all three sides equal, an isosceles triangle has at least two sides equal, and a scalene triangle has all sides of different lengths. This classification helps in understanding the properties and relationships within the triangle.

Triangle Classification Criteria

To classify a triangle accurately, one must apply the criteria for both angle and side classifications. This involves measuring the angles to determine if they are acute, right, or obtuse, and measuring the sides to see if they are equal or different. Mastery of these criteria allows for a comprehensive understanding of triangle properties and their applications in various mathematical contexts.

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