Geometry Lesson 4 2 Angles of Triangles Objective

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

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

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

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.

Find the measure of each numbered angle.

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

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

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

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

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

Corollaries Corollary 4. 1 l The acute angles of a right triangle are complementary. Corollary 4. 2 l There can be at most one right or obtuse angle in a triangle.

Find the measures of each numbered angle.

Find the measures of each numbered angle. 104 56

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