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Geometry 3 Dec 2012

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”.

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Geometry 3 Dec 2012

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  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 2nd “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. Exterior angle Vertex Side Diagonal Interior angle Polygons

  6. Equiangular: all angles have equal measure • Equilateral: all sidesare 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. 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

  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. Polygons

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

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