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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insert step 1: Identify the type of triangle based on its angles.

insert step 2: Determine if the triangle is acute, right, or obtuse by examining the measures of its angles.

insert step 3: Classify the triangle as equilateral, isosceles, or scalene by comparing the lengths of its sides.

insert step 4: Use the properties of triangles to verify your classifications.

insert step 5: Review the definitions of each type of triangle to ensure accurate classification.

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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 (all angles less than 90 degrees), right (one angle exactly 90 degrees), and obtuse (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 (all sides equal), isosceles (two sides equal), and scalene (all sides of different lengths). This classification helps in understanding the properties and relationships within the triangle, which are crucial for solving related problems.

Triangle Inequality Theorem

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This theorem is fundamental in verifying whether a set of three lengths can form a triangle and aids in classifying triangles based on their side lengths.

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