9-3 Triangles Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

9-3 Triangles Warm Up Solve each equation x + 37 = x = x + 18 = = 2x x x = 81 x = 79 x = 81 x = 36

9-3 Triangles Problem of the Day What is the one hundred fiftieth day of a non-leap year? May 30

9-3 Triangles MA.8.G.2.3 Demonstrate that the sum of the angles in a triangle is 180 degrees and apply this fact to find unknown measure of angles… Sunshine State Standards

9-3 Triangles Vocabulary Triangle Sum Theorem acute triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle

9-3 Triangles If you tear off two corners of a triangle and place them next to the third corner, the three angles seem to form a straight line.

9-3 Triangles Draw a triangle and extend one side. Then draw a line parallel to the extended side, as shown. The three angles in the triangle can be arranged to form a straight line or 180°. The sides of the triangle are transversals to the parallel lines.

9-3 Triangles An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

9-3 Triangles Additional Example 1A: Finding Angles in Acute, Right, and Obtuse Triangles Find c° in the right triangle. 42° + 90° + c° = 180° 132° + c° = 180° c° = 48° –132°

9-3 Triangles Additional Example 1B: Finding Angles in Acute, Right, and Obtuse Triangles Find m° in the obtuse triangle. 23° + 62° + m° = 180° 85° + m° = 180° m° = 95° –85° –85°

9-3 Triangles Find b° in the right triangle. 38° + 90° + b° = 180° b° = 52° 38° b°b° Check It Out: Example 1A

9-3 Triangles Check It Out: Example 1B Find x° in the right triangle. 25° + 36° + x° = 180° x° = 119°

9-3 Triangles An equilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.

9-3 Triangles Additional Example 2A: Finding Angles in Equilateral, Isosceles, and Scalene Triangles 62° + t° + t° = 180° 62° + 2t° = 180° 2t° = 118° –62° –62° Find the angle measures in the isosceles triangle. 2t° = 118° 2 t° = 59° Triangle Sum Theorem Combine like terms. Subtract 62° from both sides. Divide both sides by 2. The angles labeled t° measure 59°.

9-3 Triangles Additional Example 2B: Finding Angles in Equilateral, Isosceles, and Scalene Triangles 2x° + 3x° + 5x° = 180° 10x° = 180° x = 18° Find the angle measures in the scalene triangle. Triangle Sum Theorem Combine like terms. Divide both sides by 10. The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

9-3 Triangles Check It Out: Example 2A 2m° + 36° = 180° 2m° = 144° m° = 72° Find the angle measures in the isosceles triangle. m° 36° The angle measures are 72°, 72°, and 36°.

9-3 Triangles p° + 8° + 8p° + 34p° = 180° 43p° = 172° p° = 4° Find the angle measures in the scalene triangle. 8p°8p°P°+ 8° 34p° Check It Out: Example 2B Angle measures: = 12°, 8(4) = 32°, and 34(4) = 136°.

9-3 Triangles The second angle in a triangle is six times as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible picture. Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle measure Additional Example 3: Finding Angles in a Triangle that Meets Given Conditions

9-3 Triangles Additional Example 3 Continued x° + 6x° + 3x° = 180° 10x° = 180° x° = 18° Triangle Sum Theorem Combine like terms. Divide both sides by 10. Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 1212

9-3 Triangles X° = 18° x° = 18° 6 18° = 108° 3 18° = 54° The angles measure 18°, 54°, and 108°. The triangle is an obtuse scalene triangle. Additional Example 3 Continued Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 1212

9-3 Triangles The second angle in a triangle is twice as large as the first. The third angle measure is the average of the first two angle measures. Find the angle measures and draw a possible figure. Check It Out: Example 3

9-3 Triangles x° + 2x° + = 180° Triangle Sum Theorem x° = 180° Check It Out: Example 3 Continued x° + 2x° x° = 40° The angles measure 40°, 80°, and 60°.

9-3 Triangles 60° 40° 80° Check It Out: Example 3 Continued

9-3 Triangles Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

9-3 Triangles Lesson Quiz: Part I 1. Find the missing angle measure in the acute triangle shown. 2. Find the missing angle measure in the right triangle shown. 38° 55°

9-3 Triangles Lesson Quiz: Part II 3. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°. 50°

9-3 Triangles 1. Identify the missing angle measure in the acute triangle shown. A. 43° B. 57° C. 80° D. 90° Lesson Quiz for Student Response Systems

9-3 Triangles 2. Identify the missing angle measure in the acute triangle shown. A. 40° B. 50° C. 90° D. 180° Lesson Quiz for Student Response Systems

9-3 Triangles 3. Identify the missing angle measure in an acute triangle with angle measures of 38° and 61°. A. 38° B. 61° C. 81° D. 99° Lesson Quiz for Student Response Systems