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Section 3-4: The Polygon Angle-Sum Theorem

Section 3-4: The Polygon Angle-Sum Theorem. Goal 2.03: Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs: c) other polygons. Homework Check Matching Quiz Triangles. Essential Questions. How are polygons classified?

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Section 3-4: The Polygon Angle-Sum Theorem

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  1. Section 3-4: The Polygon Angle-Sum Theorem Goal 2.03: Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs: c) other polygons

  2. Homework Check Matching Quiz Triangles

  3. Essential Questions • How are polygons classified? • How is the sum of the measures of exterior and interior angles of convex polygons found? • How is the measure of exterior and interior angles found in a regular convex polygon?

  4. Polygons many angled (many sided) figure such that: 1. Each segment intersects exactly two other segments, one at each endpoint. 2. No two segments with a common endpoint are collinear.

  5. Convex a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.

  6. Regular polygons a convex polygon which is both equilateral and equiangular

  7. Diagonals a segment joining two nonconsecutive vertices

  8. Names of Polygons Names of polygonsNumber of sides triangle 3 quadrilateral 4 pentagon 5 hexagon 6 heptagon/septagon 7 octagon 8 nonagon 9 decagon 10 dodecagon 12 icosagon 20

  9. Together Discovery Lesson: Angles of Polygons Step 1: Write the number of sides each of the polygons has in the first column Step 2: From 1 vertex of each drawing, draw diagonals. Answer the column of # of diagonals from 1 vertex. Step 3: Complete number of triangles that are in each polygon.

  10. Step 4: There are 180° in each triangle. Use info to find the sum of the interior angles of each polygon. Step 5: Review equiangular and equilateral. What is the measure of each interior angle of the regular polygons? (Sum divided by n) Step 6: Color polygon’s exterior angles. Cut out and place a dab on the back. Place the vertices of the exterior angles in the center so all touch but do not overlap. Each should look like a circle.

  11. Step 7: Complete column “Sum of exterior angles”. All will be 360°. Step 8: Find the measure of each exterior angle. Divide 360 by n. Step 9: Do you notice anything about the interior angle measure and exterior angle measure? Step 10: Is there an easier way to find the measure of an interior angle if you know the measure of an exterior angle than finding the number f sides first and then using the formula?

  12. 65. measure of each interior angle of a convex regular polygon: (n – 2)(180) where n = 2 number of sides 66. number of diagonals that can be drawn from each vertex of a convex regular polygon: (n-3) where n = number of sides

  13. 67. total number of diagonals that can be drawn in a convex regular polygon: n(n-3) where n = number of sides 2 68.measure of each exterior angle of a convex regular polygon: 360 where n= number of sides n **Note: measure of an exterior angle + measure of an interior angle = 180

  14. P 147 1. 2. 3. 4. 5. 6. 7. 8.

  15. Review convex and nonconvex P 147: 9. 10. 11. 12. 13. 14. 15. 16. 22.

  16. Group Practice: with a partner, p. 147 (17 -21, 23 – 25) Independent Practice: p. 149 (47 – 49) Summarize: Lesson Quiz 3-4

  17. Homework Worksheet: Angles of a Triangle Angles of a Polygon

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