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1.5: Polygons

1.5: Polygons. =convex and concave. p. 514-521. GSE’s. Primary.

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1.5: Polygons

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  1. 1.5: Polygons =convex and concave p. 514-521 GSE’s Primary M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios(sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem).

  2. Polygon: a closed figure with straight sides http://en.wikipedia.org/wiki/File:Assorted_polygons.svg

  3. Polygons Not Polygons What is a Polygon ?

  4. Convex polygon: if you extend any side of the polygon, you will not go through the figure Concave polygon: the opposite is true (it caves in)

  5. Triangle Sum • The sum of the measures of the interior angles of a triangle is 180o. • mA + mB+ mC=180o + + = 180 A B C

  6. Example 1 • Name Triangle AWE by its angles mA + mW+ mE=180o (3x+5) + ( 8x+22) + (4x-12) = 180 A 15x + 15 = 180 15x = 165 x = 11 3x +5 mA = 3(11) +5 = 38o 8x + 22 mW = 8(11)+22 = 110o 4x - 12 W mE = 4(11)-12 = 32o E Triangle AWE is obtuse

  7. A B C H G D F E 1) Pick any vertex. 2) Make a darker point at it. 3) Connect that point to every other vertice in the polygon Write down how many non-overlapping triangles are formed.

  8. Exterior angle x y Extend any one side of the figure The angle formed is the exterior angle. It’s a linear pair With the inside angle

  9. Springboard p. 93 HANDOUT on investigating polygons angles Convex Polygon Number of Number of Sum of interior Sum of ext. sides ‘s Angles Angles

  10. The formula for finding the sum of the interior angles of any convex polygon is : • The sum of all exterior angles of any convex polygon is:

  11. Regular Polygons • Polygons where each angle and side is congruent What is an example of a regular 4 sided polygon? How about a 3 sided polygons?

  12. The formula for finding one interior angle in any regular polygon.

  13. Kite ABRN 80 Find the measure of angle N 120 120

  14. Solve for x in the Hexagon 110 2x 80 50 115 130

  15. The measure of one of the interior angles of a regular polygon is 160. How many sides does the regular polygon have?

  16. Homework

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