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Please make a new notebook

Please make a new notebook. It’s for Chapter 6/Unit 3 Properties of Quadrilaterals and Polygons. Then, would someone hand out papers, please? Thanks. ♥. to Unit 3 Properties of Quadrilaterals. Chapter 6 Polygons a n d Quadrilaterals. Please get: 6 pieces of patty paper protractor

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Please make a new notebook

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  1. Please make a new notebook It’s for Chapter 6/Unit 3 Properties of Quadrilaterals and Polygons Then, would someone hand out papers, please? Thanks.♥

  2. to Unit 3Properties of Quadrilaterals Chapter 6 Polygons and Quadrilaterals

  3. Please get: • 6 pieces of patty paper • protractor • Your pencil

  4. In this activity, we are going explore the interior and exterior angle measuresof polygons. Let’s define ‘polygon’ But first… The word ‘polygon’ is a Greek word. Poly means many and gon means angles What else do you know about a polygon?

  5. Let’s define ‘polygon’ What else do you know about a polygon? • A two dimensional object • A closed figure • Made up of three or more straight line segments • There are exactly two endpoints that meet at a vertex • The sides do not cross each other The word ‘polygon’ is a Greek word. Poly means many and gon means angles

  6. There are also different types of polygons: concave convex Concave polygons have at least one interior angle greater than 180◦ Convex polygons have interior angles less than 180◦

  7. M1 L1 K1 N1 O1 P1 R1 Q1 S1 U1 T1 V1 Let’s practice: • Decide if the figure is a polygon. • If so, tell if it’s convex or concave. • If it’s not, tell why not.

  8. Ok, now where were we? Oh, yes, an activity about polygons... and the interior and exterior angle measures.

  9. Draw a large scalene acute triangle on a piece of patty paper. Label the angles INSIDE the triangle as a, b, and c. 4. 1. 2. 3. 5. On another piece of PP, draw a line with your straightedge and put a point toward the middle of the line. Place the point over the vertex of angle a and line up one of the rays of the angle with the line. Trace angle a onto the second patty paper. Trace angles b and c so that angle b shares one side with angle a and the other side with angle c. Should look like this:

  10. What did you just prove about the interior angle measures of a triangle? Yep. They equal 180◦

  11. Draw a quadrilateral on another PP. Label the angles a, b , c, and d. 4. 1. 2. 3. 5. Draw a point near the center of a second PP and fold a line through the point. Place the point over the vertex of angle a and line up one of the rays on the angle with the line. Trace angle a onto the second PP. Trace angle b onto the second PP so that a and b are sharing the vertex and a side Repeat with angles c and d.

  12. What did you just prove about the interior angle measures of a quadrilateral? Yep. They equal 360◦

  13. Can you find the pattern? Tresmas… 1. 2. Can you create an equation for the pattern? Repeat these steps for a pentagon. Remember to figure the sum of the interior angles. Repeat these steps for a hexagon. Remember to figure the sum of the interior angles. Put this table in your notes and complete it: 180 360 540 720 900 1080

  14. Behold… = total sum of the interior angles of a polygon (The number of sides of a polygon – 2)(180) (n – 2)(180) Or, as we mathematicians prefer to say…

  15. 180o 180o 180o 180o 2 1 diagonal 3 x 180o = 540o 180o 5 180o 180o 180o 180o 180o 4 sides Quadrilateral 5 sides Pentagon 2 x 180o = 360o 3 2 diagonals 180o 180o 180o 180o 6 sides Hexagon Heptagon/Septagon 7 sides 4 x 180o = 720o 4 5 x 180o = 900o 3 diagonals 4 diagonals Polygons

  16. On your PP with the triangle, extend each angle out to include the exterior angle. • Measure and record each linear pair. • What is the total sum of the exterior angles? • Do the same with the quadrilateral, pentagon and hexagon. • Remember to record each linear pair. • Can you make a conjecture as to the sum of exterior angles? 3. 360 360 360 360 360 360

  17. You have just proven two very important theorems: TADA! Polygon Angle-Sum Theorem • (n-2) 180 Polygon Exterior Angle-Sum Theorem • Always = 360◦

  18. A quick polygon naming lesson: I ♥ Julius and Augustus

  19. A regular polygon is equilateral and equiangular Pentagon Square Hexagon Triangle Heptagon Dodecagon Octagon Nonagon

  20. Let’s practice: How would you find the total interior angle sum in a convex polygon? How would you find the total exterior angle sum in a convex polygon? What is the sum of the interior angle measures of an 11-gon? What is the sum of the measure of the exterior angles of a 15-gon? Find the measure of an interior angle and an exterior angle of a hexa-dexa-super-double-triple-gon. Find the measure of an exterior angle of a pentagon. The sum of the interior angle measures of a polygon with n sides is 2880. Find n. (n-2)(180) The total exterior angle sum is always 360◦ 1620◦ 360◦ 180◦ 360/5 = 72 ◦ 2880 = (n-2)(180) n = 18 sides

  21. Assignment pg 356 7 – 27, 29-35 40-41, 49-54

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