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EXAMPLE 1

a. Classify XYZ by its angles. Classify XYZ by its side lengths. b. a. The triangle has a right angle at Y . So, it is a right triangle. b. The triangle has two sides of equal length. So, it is an isosceles triangle. EXAMPLE 1. Classifying a Triangle. SOLUTION.

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EXAMPLE 1

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  1. a. Classify XYZ by its angles. Classify XYZ by its side lengths. b. a. The triangle has a right angle at Y. So, it is a right triangle. b. The triangle has two sides of equal length. So, it is an isosceles triangle. EXAMPLE 1 Classifying a Triangle SOLUTION

  2. From the diagram below you can see that the sum of the angle measures in the triangle is 180. This is true for any triangle. EXAMPLE 1 Classifying a Triangle Angles in a Triangle

  3. Find the value of x. Then classify the triangle by its angles. The sum of the angle measures of a triangle is 180. x + 42 + 42 = 180 x + 84 = 180 ANSWER The value of xis 96. The triangle has one obtuse angle, so it is an obtuse triangle. EXAMPLE 2 Finding an Unknown Angle Measure SOLUTION Write an equation. Add. x + 84 – 84 = 180 – 84 Subtract 84 from each side. x = 96 Simplify.

  4. Classify the triangle by its side lengths. 1. 7 cm, 9 cm, 7 cm ANSWER The triangle has two sides of equal length. So, it is an isosceles triangle. 2. 11 ft, 11 ft, 11 ft ANSWER The triangle has all its sides equal. So, it is an equilateral triangles. for Example 1 and 2 GUIDED PRACTICE

  5. 3. 4 in., 5 in., 6 in. ANSWER All the sides of the triangles are of different length. So, it is an scalene triangle. 4. 6 ft, 6 ft, 6 ft ANSWER The sides of the triangles are equal. So, it is an equilateral triangle. for Example 1 and 2 GUIDED PRACTICE Classify the triangle by its side lengths.

  6. 5. 10 mm, 10 mm, 8 mm ANSWER The triangle has two sides of equal length. So, it is an isosceles triangle. 6. 2 cm, 8 cm, 7 cm ANSWER All the sides of the triangles are of different length. So, it is an scalene triangle. for Example 1 and 2 GUIDED PRACTICE Classify the triangle by its side lengths.

  7. 7. Find the value of x. Then classify the triangle by its angles. ANSWER The value of xis 52 . The triangle has all the acute angle, so it is an acute triangle. for Example 1 and 2 GUIDED PRACTICE

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