7-2: Exterior Angle Theorem

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Presentation transcript:

7-2: Exterior Angle Theorem

7-2: Exterior Angle Theorem Exterior Angle: An angle of a triangle that forms a linear pair with one of the angles of the triangle. Remote Interior Angles: The angles that do not form a linear pair with the exterior angle. Remote Interior Angle Exterior Angle

7-2: Exterior Angle Theorem Identify each exterior angle. Then, identify the remote interior angles Note that each exterior angle at a vertex share the same interior angles Exterior Angle Remote Interior Angles 4 2 & 3 5 1 & 3 6 7 1 & 2 8 9

7-2: Exterior Angle Theorem Theorem 7-3 (Exterior Angle Theorem): The measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles. 4 = 1 + 2 Discuss Proof 4 1 2 3

7-2: Exterior Angle Theorem If m2 = 38 and m4 = 134, what is m5? 4 = 2 + 5 134 = 38 + 5 96 = 5 If m2 = x + 17, m3 = 2x, and m6 = 101, find the value of x. 6 = 2 + 3 101 = x + 17 + 2x 101 = 3x + 17 84 = 3x 28 = x

7-2: Exterior Angle Theorem Your Turn What is 1 if m3 = 46 and m5 = 96? 142 If m2 = 3x, m3 = x + 34, and m6 = 98, find the value of x. Then, find m3. x = 16 m3 = 50

7-2: Exterior Angle Theorem Two “common sense” theorems are derived from the Exterior Angle Theorem. Theorem 7-4: The measure of an exterior angle of a triangle is greater than the measure of either of its two remote interior angles. Theorem 7-5: If a triangle has one right angle, then the other two angles must be acute.

7-2: Exterior Angle Theorem Assignment Worksheet #7-2