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LESSON 4.1 NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 194–201 GOAL Classify triangles by their sides and angles and find angle measures in triangles VOCABULARY A triangle is a figure formed by three segments joining three noncollinear points. An equilateral triangle has three congruent sides. An isosceles triangle has at least two congruent sides. A scalene triangle has no congruent sides. An acute triangle has three acute angles. An equiangular triangle has three congruent angles. A right triangle has one right angle. An obtuse triangle has one obtuse angle. The three angles of a triangle are the interior angles. When the sides of a triangle are extended, the angles that are adjacent to the interior angles are exterior angles. Theorem 4.1 Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180. Theorem 4.2 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary. Chapter 4 Copyright © McDougal Littell Inc. All rights reserved. Geometry Practice Workbook with Examples 61 LESSON 4.1 CONTINUED EXAMPLE 1 NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 194–201 Classifying Triangles Classify the triangles by their sides and angles. a. b. L Z 20 45 23 5.7 19 J 50 110 16 4 K 45 X 4 Y SOLUTION a. JKL has one obtuse angle and no congruent sides. It is an obtuse scalene triangle. b. XYZ has one right angle and two congruent sides. It is a right isosceles triangle. Exercises for Example 1 Classify the triangle by its sides and angles. 1. 2. 3. 30 60 30 5 5.8 17 10 120 17 18 10 30 60 60 17 Chapter 4 2.9 60 62 Geometry Practice Workbook with Examples Copyright © McDougal Littell Inc. All rights reserved. LESSON 4.1 CONTINUED EXAMPLE 2 NAME _________________________________________________________ DATE ____________ Practice with Examples For use with pages 194–201 Finding Angle Measures a. Find the value of x. b. Find the value of y. (4x 5) 2y (3x 11) 50 SOLUTION a. From the Corollary to the Triangle Sum Theorem, you can write and solve an equation to find the value of x. 4x 5 3x 11 90 x 12 The acute angles of a right triangle are complementary. Solve for x. b. You can apply the Exterior Angle Theorem to write and solve an equation that will allow you to find the value of y. 90 50 2y Apply the Exterior Angle Theorem. y 70 Solve for y. Exercises for Example 2 Find the value of x. 4. 3x 30 5. x 8x 2x Chapter 4 Copyright © McDougal Littell Inc. All rights reserved. Geometry Practice Workbook with Examples 63