1 / 17

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?

marin
Download Presentation

Section 3-4: The Polygon Angle-Sum Theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related