1. Geometry 3 Dec 2012 1) Empty folders and place papers in correct section in your binder. 2) Place book and binder on your desk. 3) DO Flow Chart Proof Handout, # 3 Finished? Do 4.6 CPCTC handout, #12. Finished? Choose one proof from handout and rewrite in a 2 nd “style”.

2. objective Students will apply polygon interior and exterior sum conjectures to find angle measures. Students will take notes, work collaboratively and present to the class.

3. Homework due Dec 4 5.1, pg 259: 3 – 8 5.2, pg. 264: 8 – 13, 16, 17

4. Inductive Reasoning the process of OBSERVING FINDING PATTERNS MAKING GENERALIZATIONS… GEOMETRY  the generalization is called A CONJECTURE!!! Conjecture is an IF…THEN… statement

5. Interior angle Diagonal Vertex Side Exterior angle Polygons

6. Equiangular: all angles have equal measure Equilateral: all sides are the same length Polygons

7. Regular Polygon: a polygon where all the angles are equal and all of the sides are the same length. They are both equilateral and equiangular Polygons

8. Examples of Regular Polygons Polygons

9. Exterior Angles of a Polygon Is there a pattern for the sum for exterior angles of polygons? DEMONSTRATION What about a octagon? What is the measure of ONE exterior angle for a regular quadralateral? regular pentagon? http://math.kendallhunt.com/x19427.html

10. No matter what type of polygon we have, the sum of the exterior angles is ALWAYS equal to 360º. Sum of exterior angles = 360º Polygons

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

12. Rule? Can you find a rule for the interior angle sum for an “N”-gon? What if you have a regular polygon? Regular Polygon- all sides and angles have the same measure

13. Term Definition Example Polygon Sum Conjecture The sum of the measures of the interior angles of an n-gon is Sum of interior angles Exterior angle sum conjecture For any polygon, the sum of the measures of a set of external angles is 360 0 Equiangular Polygon Conjecture Each interior angle of an equiangular n-gon Polygons

14. 2 x 180 o = 360 o 360 – 245 = 115 o 3 x 180 o = 540 o 540 – 395 = 145 o y 117 o 121 o 100 o 125 o 140 o z 133 o 137 o 138 o 125 o 105 o Find the unknown angles below. Diagrams not drawn accurately. 75 o 100 o 70 o w x 115 o 110 o 75 o 95 o 4 x 180 o = 720 o 720 – 603 = 117 o 5 x 180 o = 900 o 900 – 776 = 124 o Polygons

15. Practice– Homework Problems CW Focus: In progress: 5.1: 3, 4 5.2: 8 Partial: 5.1: 5, 6 5.2: 9 Complete: 5.1: 7, 8 5.2: 10 Advanced: 5.1: 7 5.2: 10, 13

16. Debrief What is difficult about finding angle measures in an “angle chase”? What strategies can you use? What is easy?