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Understanding Triangle Angle Theorems

Learn to apply the Triangle Angle-Sum Theorem, Exterior Angle Theorem, and how to find numbered angles with auxiliary lines. Practice finding exterior angles and remote interior angles using the relevant theorems. Solve angle calculations with provided examples and identify corollaries associated with triangles. Homework exercises included.

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Understanding Triangle Angle Theorems

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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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