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Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 Lesson 72 Angles Theorems for 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. Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 Draw a triangle and extend one side. Then draw a line parallel to the extended side, as shown. The sides of the triangle are transversals to the parallel lines. The three angles in the triangle can be arranged to form a straight line or 180°. The angle measures of a triangle in a plane add up to 180 0 . Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 The angle measures of a triangle in a plane add up to 180 0 . o m A + m B + m C = 180 The angle measures of a triangle in a plane add up to 180 0 . o m A + m B + m C = 180 This is called the Triangle Sum Theorem. Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 The angle measures of a triangle in a plane add up to 180 0 . o m A + m B + m C = 180 This is called the Triangle Sum Theorem. o o o 42 + 103 + 35 = 180 o 42 o 103 o 35 What do you remember about triangles? o Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 What do you remember about triangles? An acute triangle has 3 acute angles. An acute triangle has 3 acute angles. A right triangle has 1 right angle. Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle. Find p° in the acute triangle. Remember: There are 3 acute angles. 73° + 44° + p° = 180° 117° + p° = 180° –117° –117° p° = 63° Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 Find c° in the right triangle. Don't forget a right triangle has only 1 right angle. c = _____ Find c° in the right triangle. Find m° in the obtuse triangle. Hint: An obtuse triangle Don't forget a right triangle has has only 1 obtuse angle. only 1 right angle. c m = _____ = _____ Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 An equilateral triangle has 3 congruent sides and 3 congruent angles. Find the angle measures in the equilateral triangle. 3b° = 180° Triangle Sum Theorem An isosceles triangle has at least 2 congruent sides and 2 congruent angles. Find the angle measures in the isosceles triangle. 62° + t° + t° = 180° Triangle Sum Theorem A scalene triangle has no congruent sides and no congruent angles. Find the angle measures in the scalene triangle. What do I do here? Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 A scalene triangle has no congruent sides and no congruent angles. Find the angle measures in the scalene triangle. 2x° + 3x° + 5x° = 180° practice Triangle Sum Theorem Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 Finding Angles in a Triangle Meets that Given Conditions Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 Finding Angles in a Triangle Meets that Given Conditions o Let x = the first angle measure. x° + 6x° + 3x° = 180° Finding Angles in a Triangle Meets that Given Conditions o Let x = the first angle measure. o Then 6x = second angle measure. x° + 6x° + 3x° = 180° Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 Finding Angles in a Triangle Meets that Given Conditions Solve for x. o Let x = the first angle measure. x° + 6x° + 3x° = 180° o Then 6x = second angle measure. o 1 (6x ) = 3x, or third angle measure. 2 Continued So x = ________ Now find the angle measurements of each angle in the triangle. x° = the first angle measure. 6x° = second angle measure o 18 Click 108o Click 3x° = third angle measure 54o Click Adv Lesson 7.2 Angle Theorems for Triangles.notebook January 18, 2017 Now you try it..... The second angle in a triangle is three times larger than the first. The third angle is one third as large as the second. Find the angle measures and draw a possible picture. o o o 1st 2nd 3rd 36 108 36 Homework Worksheet 7.2 (Both Sides) Quiz Friday