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 and Quadrilaterals

Please get: 6 pieces of patty paper protractor Your pencil

In this activity, we are going explore the interior and exterior angle measures of 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?

Poly means many and gon means angles 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

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◦

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. K1 L1 M1 N1 O1 P1 Q1 R1 S1 T1 V1 U1

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

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

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

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

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

Can you find the pattern? Can you create an equation for the pattern? Tres mas… Can you create an equation for the pattern? 1. Repeat these steps for a pentagon. Remember to figure the sum of the interior angles. 2. Repeat these steps for a hexagon. Remember to figure the sum of the interior angles. Put this table in your notes and complete it: Number of sides of the polygon 3 4 5 6 7 8 Sum of the interior angle measures 180 360 540 720 900 1080

total sum of the interior angles of a polygon 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…

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

Measure and record each linear pair. 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. Number of sides of the polygon 3 4 5 6 7 8 Sum of the interior angle measures 180 360 540 720 900 1080 Sum of the exterior angle measures 360 360 360 360 360 360

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

A quick polygon naming lesson: # of sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon/Septagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon I ♥ Julius and Augustus

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

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

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