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7.1 More Triangle Theorems

7.1 More Triangle Theorems. Objectives: Know and use theorems about interior and exterior angles in triangles Know and use midline theorem. Theorem 50: The sum of the measure of the three angles of a triangle is 180° . 1. 3. 2. 5. 4. m Ð2 + m Ð 4 + m Ð 5 = 180°. 4.

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7.1 More Triangle Theorems

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  1. 7.1 More Triangle Theorems • Objectives: • Know and use theorems about interior and exterior angles in triangles • Know and use midline theorem

  2. Theorem 50: The sum of the measure of the three angles of a triangle is 180° 1 3 2 5 4 mÐ2 + mÐ4 + mÐ5 = 180°

  3. 4 Exterior Angle of a polygon is an angle that is adjacent to and supplementary to an interior angle of the polygon.

  4. Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. 1 2 3 4 mÐ4 = mÐ1 + mÐ3

  5. Theorem 52 (Midline Thm): If a segment joins the midpoints of two sides of a triangle, then it is parallel to the third side, and its length is ½ the length of the third side. A D E C B

  6. Theorem 52 (Midline Thm): If a segment joins the midpoints of two sides of a triangle, then it is parallel to the third side, and its length is ½ the length of the third side. F A D E C B

  7. Example 1: Findx, y, and z. 80° 100° z° y° 55° x° 60° x = 20°, y = 45°, z = 115°

  8. Example 2: If the ratio of angles of a triangle is 5:6:7, find the measures of the angles. 50°, 60°, 70°

  9. Example 3: Given: D & E are midpoints of mÐCDE = (3x - 6)°; mÐA = (6y + 6)°; mÐCED = (2x + 6)°; mÐB = (5y + 5)° Find:mA, mB, and mC. C E D 60°, 50°, 70° A B

  10. Example 4: Given: D and E are midpoints of , respectively. If AB = x² + 3 and DE = x + 9, find DE. C DE = 6 or 14 E D A B

  11. Example 5: If one of the angles of a triangle is 80°, find the measure of the angle formed by the bisectors of the other two angles. A 80° mE = 130 E y° x° y° x° B C

  12. Example 6: Given: mÐ1 = 150°and mDis 10 less than 3 timesmE. Find the measure of each angle of the triangle. D 1 E F

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