Geometry 13 January 2014 Warm Up- (keep pink sheets in left side ) 1) Correct Homework √ or X EACH PROBLEM. a) Work with your group to IDENTIFY and CORRECT ERRORS. √ or X EACH PROBLEM. b) Please do MORE than just write the ‘correct’ answer…. HOW do you get it!!? Show the WORK to SUPPORT the correct answer! 2) Do #11 Flowchart Proof HANDOUT

objective Students will develop, prove and apply polygon interior and exterior sum conjectures. Students will take notes, work collaboratively and present to the class.

Homework: DUE TODAY: pg. 259+: 3 – 10 Start with sketch. Clearly show K’s and W’s. CHECK YOUR ANSWERS. DUE SUNDAY/ Monday- KHAN ASSIGNMENT DUE FRIDAY, January 17: pg. 264: 7, 8, 10, 16 pg. 271: 1 – 8 FINISH 5.2 HANDOUT (both sides)

Write in your Notes 1)EXPLAIN in writing THINK-PAIR- SHARE WHAT are THREE DIFFERENT METHODS that could be used to find the interior angle sum of any polygon? 2) USE at least 2 different methods to find the missing interior angle sum of a hexagon. Clearly show your thinking.

Method- divide the polygon into non- intersecting triangles

Method- triangles with common vertex somewhere inside polygon Interior angle sum = 180n - 360

Method- develop/use the rule

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 Equiangular Polygon Conjecture Each interior angle of an equiangular n-gon Polygons

Prove Exterior Angle Sum PROOF Algebraic Proof

Practice Do PROOF- two methods- HANDOUT Start with words… divide the polygon into….. KHAN QUIZ– when finished you may begin work on: Do Lesson 5.2 Handout (finish for homework) Be ready to share your work with the class.

Practice- Angle Chase, #12 Calculate the measure of each lettered angle measure. Explain how you found your answer. Show brief calculation and relationship. Triangle Sum: a + b + 34 = 180 Quadrilateral Sum, LP, VA, CA, etc. Be ready to share a PART of the puzzle with the class!!

Debrief What different methods can you use to find the interior angle sum of any polygon? What is the exterior angle sum for any polygon?

Geometry 14 January 2014 Warm Up DO Four Pentagons Handout Please work independently We will discuss your work with a partner later in the week.

objective Students will develop, prove and apply polygon interior and exterior sum conjectures. Students will take notes, work collaboratively and present to the class.

DUE FRIDAY, January 17: pg. 264: 7, 8, 10, 16 pg. 271: 1 – 8 FINISH 5.2 HANDOUT (both sides) NO SCHOOL next Monday, January 20 DUE Monday/ Tuesday- KHAN ASSIGNMENT

Method- divide the polygon into non- intersecting triangles

Method- triangles with common vertex somewhere inside polygon Interior angle sum = 180n - 360

Method- develop/use the rule

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 Equiangular Polygon Conjecture Each interior angle of an equiangular n-gon Polygons

Practice- Angle Chase, #12 Calculate the measure of each lettered angle measure. Explain how you found your answer. Show brief calculation and relationship. Triangle Sum: a + b + 34 = 180 Quadrilateral Sum, LP, VA, CA, etc. Be ready to share a PART of the puzzle with the class!!

Practice Do Lesson 5.2 Handout – BOTH SIDES (finish for homework) Be ready to share your work with the class.

Debrief How can you find the measures of interior angles of regular polygons if no measures are given?

Geometry 15/16 January WARM UP 1) Do work on finding angle measures on handout 2) FINISHED? WORK ON 5.2 handout- focus #7 QUESTIONS?

objective Students will explore properties of kites and trapezoids. Students will take notes, work collaboratively and present to the class.

DUE FRIDAY, January 17: pg. 264: 7, 8, 10, 16 pg. 271: 1 – 8 FINISH 5.2 HANDOUT (both sides) NO SCHOOL next Monday, January 20 DUE Monday/ Tuesday- KHAN ASSIGNMENT

Syllabus REVIEW briefly– homework policy late work policy BRING BACK signed pink slip for 8 easy homework points---- I’ll accept them through Friday, Jan 24

Summarizing Properties of Quadrilaterals Quadrilateral KiteParallelogramTrapezoid RhombusRectangle Square Isosceles Trapezoid

Review Quadrilateral DEFINITIONS Use graphic organizer. WRITE definitions for each quadrilateral. MARK each figure with notation showing the definition.

Is a cow ALWAYS a mammal? Is a mammal ALWAYS a cow? A square (ALWAYS, SOMETIMES, NEVER) a parallelogram. A parallelogram (ALWAYS, SOMETIMES, NEVER) a square. examples: 1) A kite is ALWAYS a __________________. 2) A parallelogram is SOMETIMES a ______________. 3) A square is ALWAYS a _____________. 4) A rectangle is ______________a square.

Geometry Properties of Polygons see page 268– read together

add sketch to graphic

Using properties of kites A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

What about kites? Are there any relationships with the angles? Are any congruent? What about the diagonals? Do they bisect each other? Do they Bisect angles?

read about trapezoids- pg. 269 read together

Using properties of trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel sides.

special quadrilaterals- see pg. 64+ Trapezoid: a quadrilateral with exactly one pair of parallel sides Isosceles Trapezoid: a trapezoid with non- parallel sides congruent

What about trapezoids? Are any angles the same measure? What about isosceles trapezoids? Angles? Do you notice anything with the diagonals. What relationships can you find?

Investigations pg Fill in your graphic organizer as we do the patty paper investigations on polygon properties. All students will do the investigations in sections 5.3 – 5.6, summarizing your conjectures with sketches and related vocabulary on the handout. Expectations- do your work on a separate paper/ patty paper and attach to the handout. Label each paper with page and investigation title.

THINK- PAIR-SHARE THINK- LIST all the congruencies and properties you can find that are true with your KITE EXAMPLE- segmentKT bisects angle EKI PAIR- work with a partner to add to list GROUP– who found the most? +1 cw point

Kite Properties

Isosceles Trapezoids

Debrief Is a kite always a quadrilateral? Is a quadrilateral always a kite? What special properties does a kite have? What about a trapezoid?

Geometry 17 January )CHECK homework √ or X each problem DUE TODAY, January 17: pg. 264: 7, 8, 10, 16 pg. 271: 1 – 8 FINISH 5.2 HANDOUT (both sides) Work with a partner to identify and CORRECT your work to support the correct answer 2) Done? Sketch a kite and an isosceles trapezoid. MARK all you know to be true on the diagram (congruent parts? 90⁰? Bisect?)

Objective Students will show understanding of polygon sums and kite/ trapezoid properties on a quiz. NO SCHOOL next Monday, January 20 DUE Monday/ Tuesday- KHAN ASSIGNMENT notes on videos exercises

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 Equiangular Polygon Conjecture Each interior angle of an equiangular n-gon Polygons

QUIZ Do you best. Work silently. FINISHED? Begin to work on the PROOF handout.