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Geometry

Geometry. Lesson 4 – 2 Angles of Triangles. Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem. Triangle Angle-Sum Theorem. Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180. Auxiliary line.

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Geometry

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  1. Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

  2. Triangle Angle-Sum Theorem • Triangle Angle-Sum Theorem • The sum of the measures of the angles of a triangle is 180.

  3. Auxiliary line • Auxiliary line – an extra line or segment drawn in a figure to help analyze geometric relationships.

  4. Find the measure of each numbered angle. Which angle do we find first? Could find angle 2 first since we Know 2 other angles in that triangle. Or we could find angle 1 since we Know it forms a linear pair with 57. Since linear pair. Don’t get this 180 confused with adding all the angles of a triangle to 180.

  5. Find the measure of each numbered angle.

  6. Exterior & Remote interior angles • Exterior angles of a triangle: • Formed by one side of the triangle and the extension of an adjacent side. • Exterior angle that is adjacent to the triangle. • Remote Interior angles • The 2 interior angles inside the triangle that are not adjacent to the exterior angle.

  7. Name an exterior angle and the pair of remote interior angles that go with it. 5 4 6 3 Exterior Remote Int. 7 12 1 2 9 11 8 10 Angles 5, 8, and 11 are not exterior angles since they are not adjacent to a side of the triangle.

  8. Theorem • Exterior Angle Theorem • The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

  9. Find the measure of angle FLW. 2x – 48 = x + 32 Exterior angle = Sum of Remote Interior angles x – 48 = 32 x = 80

  10. Corollary • Corollary – • A theorem with a proof that follows as a direct result of another theorem.

  11. Corollaries • Corollary 4.1 • The acute angles of a right triangle are complementary. • Corollary 4.2 • There can be at most one right or obtuse angle in a triangle.

  12. Find the measures of each numbered angle.

  13. Find the measures of each numbered angle. 104 56

  14. Homework • Pg. 248 1 – 11 all, 12 – 40 EOE, 50, 60, 64, 66

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