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Understanding Triangle Angles: Angle-Sum and Exterior Angle Theorems

This lesson focuses on the fundamental properties of triangle angles, specifically Theorem 4.1, which states that the sum of the measures of a triangle's interior angles is always 180°. We will explore how to find missing angle measures with examples, as well as the concept of exterior angles detailed in Theorem 4.2. Each exterior angle equals the sum of the measures of the two non-adjacent interior angles. The session also includes important corollaries relating to right and obtuse triangles, followed by homework exercises for practice.

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Understanding Triangle Angles: Angle-Sum and Exterior Angle Theorems

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Presentation Transcript

  1. Geometry 4.2: Angles of Triangles

  2. Theorem 4.1: Triangle Angle-Sum • The sum of the measures of the angles of a triangle is 180°.

  3. Example 1 • : Find the missing measures. 40° 35° 1 2 38° 3

  4. Any triangle has 3 interior angles. • Triangles also have exterior anglesformed by extending one side and its adjacent side. • Each exterior angle has two remote interior anglesthat are not adjacent to it.

  5. Theorem 4.2: Exterior Angle • The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

  6. Example 2 F L 2x -48 W 32 x

  7. Corollaries • Corollary- a theorem with proof that follows as a direct result of a another theorem. • 4.1: The acute angles of a right triangle are complementary. • 4.2: There can be at most one right or obtuse angle in a triangle.

  8. Homework • Page 249: 1-33 all, 36-40 all

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