EXAMPLE 1 Classifying a Triangle a.Classify XYZ by its angles. b. Classify XYZ by its side lengths. SOLUTION a. The triangle has a right angle at Y. So,

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EXAMPLE 1 Classifying a Triangle a.Classify XYZ by its angles. b. Classify XYZ by its side lengths. SOLUTION 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.

Angles in a Triangle EXAMPLE 1 Classifying a Triangle 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 2 Finding an Unknown Angle Measure Find the value of x. Then classify the triangle by its angles. SOLUTION The sum of the angle measures of a triangle is 180. x = 180 x + 84= 180 x + 84 – 84 = 180 – 84 x = 96 Write an equation. Add. Subtract 84 from each side. Simplify. ANSWER The value of x is 96. The triangle has one obtuse angle, so it is an obtuse triangle.

GUIDED PRACTICE for Example 1 and 2 Classify the triangle by its side lengths. 1.7 cm, 9 cm, 7 cm The triangle has two sides of equal length. So, it is an isosceles triangle. ANSWER ft, 11 ft, 11 ft The triangle has all its sides equal. So, it is an equilateral triangles. ANSWER

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

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

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