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4.1 Apply Triangle Sum Properties

4.1 Apply Triangle Sum Properties. Objectives: To classify triangles by sides and angles To find the measures of the interior and exterior angles of a triangle. Polygons.

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4.1 Apply Triangle Sum Properties

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  1. 4.1 Apply Triangle Sum Properties Objectives: • To classify triangles by sides and angles • To find the measures of the interior and exterior angles of a triangle

  2. Polygons A closed plane figure is a polygon if it is formed by 3 or more line segments (sides), joined endpoint to endpoint (vertices) with each side intersecting exactly two others.

  3. 3-D Rendering 3-D rendering in digital graphics is based upon polygons.

  4. Vocabulary In your notebook, define each of these types of triangles without your book. Draw a picture for each word and leave a bit of space for additions and revisions. Classified by Sides Classified by Angles

  5. Types of Triangles

  6. Triangles in Architecture

  7. Triangles in Architecture

  8. Interior vs. Exterior Angles All the angles inside the triangle are called interiorangles. If you extend the sides of the triangle, then the angles that form a linear pair with the interior angles are called exterior angles.

  9. Investigation 1 Click on the button to investigate the Triangle Sum Theorem.

  10. Triangle Sum Theorem The sum of the measures --?--. Click the arrow buttons to watch the Flash animation of the Triangle Sum Theorem. Write and complete this statement in your notebook

  11. Example 1 In ABC below, find the measures of  1 and 2. <1 = 80 <2 = 100

  12. Example 2 Prove the Triangle Sum Theorem. Given: ABC Prove: ma + mb + mc = 180° HINT: Uses parallel lines theorem and linear angle sum TRY THIS in your notebook!

  13. Non-Euclidean Triangles Does the Triangle Sum Conjecture hold true in either hyperbolic or elliptic geometry? The answer may reveal secrets of the universe. Hyperbolic Elliptic

  14. Big Unanswered Question So what shape is the universe? Is it basically flat, or is it curved?

  15. Big Unanswered Question So what shape is the universe? Is it basically flat, or is it curved?

  16. Example 3 In the right triangle below, what is the value of x + y? 45

  17. Triangle Sum Theorem Corollary The acute angles of a right triangle are complementary.

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

  19. Example 4 Find m<JKL. m<JKL = 35

  20. Example 5 Find the values of a, b, and c. <a = 65 <b = 60 <c = 55

  21. Exercise 6: SAT What is the value of c? 160

  22. Example 7 Rewrite the Triangle Sum Theorem and its Corollary in terms of radians. Do this in your notebook

  23. Example 8 Find the measure of each angle in radians. <A & <C = 2π 7 <B = 3π 7

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