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Lesson 10-3 Triangles Line Segment – part of a line containing two endpoints Triangle – the union of three line segments that intersect only at their endpoints Vertex – is the point where the line segments of a triangle intersect The sum of the measures of the interior angles in a triangle equals 180 degrees. Example 1 Find Angle Measures Find the value of x in △ABC. mA + mB + mC = 180 x + 54 + 62 = 180 x + 116 = 180 x + 116 – 116 = 180 – 116 x = 64 Write an equation. Substitution Simplify. Subtract 116 from each side. Simplify. The measure of A is 64 Example 2 Use Ratios to Find Angle Measures The measures of the angles of △RST are in the ratio 1:3:5. What are the measures of the angles? Words The sum of the measures is 180. Variables Let x represent the measure of the first angle, 3x the measure of the second angle, and 5x the measure of the third angle. Equation x + 3x + 5x = 180 x + 3x + 5x = 180 9x = 180 9x 180 = 9 9 x = 20 Write the equation. Combine like terms. Divide each side by 9. Simplify. Since x = 20, 3x = 3(20) or 60, and 5x = 5(20) or 100. The measures of the angles are 20, 60, and 100. Classifying Angles – angles can be classified by their measure Acute – an angle with measure less than 90 degrees Right – an angle with measure equal to 90 degrees Obtuse – an angle with measure great than 90 degrees and less than 180 degrees Straight – an angle with measure equal to 180 degrees Real-World Example 3 Classify Angles DESIGN A lightening bolt design is shown at the right. What type of angle is L? M L 64 mL < 90. So, L is an acute angle. N Triangles are classified by their angles and their sides. Classifying by angles: acute, right, and obtuse Classifying by sides: scalene, isosceles, and equilateral Example 4 Classify Triangles Classify each triangle by its angles and by its sides. a. Angles: Sides: ABC has one obtuse angle. ABC has no congruent sides. The triangle is an obtuse scalene triangle. b. 12 cm 12 cm Angles: Sides: The triangle is a right isosceles triangle. The triangle has a right angle. The triangle has two congruent sides.