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Angles of Triangles and Theorems

Learn about the Angle Sum Theorem, Third Angle Theorem, Exterior Angle Theorem, and Remote Interior Angles in triangles. Practice finding missing angle measures and applying the theorems.

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Angles of Triangles and Theorems

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  1. Lesson 4-2 Angles of Triangles

  2. Ohio Content Standards:

  3. Ohio Content Standards: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

  4. Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

  5. Theorem 4.1Angle Sum Theorem

  6. Theorem 4.1Angle Sum Theorem The sum of the measures of the angles of a triangle is 180.

  7. Find the missing angle measures. 43° 79° 2 1 74° 3

  8. Theorem 4.2Third Angle Theorem

  9. Theorem 4.2Third Angle Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

  10. Exterior Angle

  11. Exterior Angle Angle formed by one side of a triangle and the extension of another side.

  12. Exterior Angle Angle formed by one side of a triangle and the extension of another side. 1

  13. Remote Interior Angles

  14. Remote Interior Angles Interior angles of the triangle not adjacent to a given exterior angle.

  15. Remote Interior Angles Interior angles of the triangle not adjacent to a given exterior angle. 2 3

  16. Theorem 4.3Exterior Angle Theorem

  17. Theorem 4.3Exterior 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.

  18. Find the measure of each numbered angle in the figure. 38° 32° 4 5 3 1 2 41° 64° 29°

  19. B C 20° A

  20. Assignment:Pgs. 189-191 11-35 all, 56-58 evens

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