Geometry 12/13 December 2012

1. Geometry 12/13 December 2012 • Place binder and text on desk. • Do warm up. Do proof “strip”. Complete back of pink sheet, summarizing polygon properties. Finished? Do pg. 301: 2

2. objective Students will explore and apply polygon properties. Students will work collaboratively to do investigations, write conjectures and apply properties to solve problems.

3. TEST- proofs, polygon properties TODAY Semester Review Packet due on your final exam day P2- Monday, December 17 P3- Tuesday, December 18 P5 and P6- Wednesday, December 19

4. Polygon PropertiesCHALLENGE I’ll call out the name of a polygon. You have 30 seconds to mark all congruencies, angles, etc, you know about the polygon. Time up? Trade papers with a partner. Partner has 30 seconds to ADD any additional information. WHOLE CLASS review– anything else? REPEAT!!! 

5. Kite Properties

6. Triangle Midsegment The segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side and is half as long.

7. Isosceles Trapezoids

8. if a quadrilateral is a parallelogram • opposite sides are parallel (DEFINITION) • opposite sides are congruent • opposite angles are congruent • consecutive angles are supplementary • diagonals bisect each other

9. Definitions…..finish Rectangle- an equiangular parallelogram Rhombus- an equilateral parallelogram Square- an equilateral, equiangular parallelogram

10. Rectangle Properties All properties of a parallelogram AND: • Diagonals are congruent • All angles are congruent (90⁰)

11. Rhombus Properties Rhombuses share all properties of a parallelogram AND: (1) Consecutive sides of a rhombus are congruent. (2) The diagonals of a rhombus bisect pairs of opposite angles. (3) The diagonals of a rhombus are perpendicular.

12. Square Properties Squares share all properties of a parallelogram AND rectangles AND rhombus CAN YOU NAME all the properties?

13. Examples The midsegment of the trapezoid is ST. Find the value of x. 8 11 S T 11 = ½ (8 + x) 22 = 8 + x 14 = x x

14. TIMED practice Each of the following seven review slides is timed. Write your answers for the multiple choice questions on your paper. Briefly write your work/ answer and see how you do!!

15. Review 1 • A polygon with 7 sides is called a ____. A) nonagon B) dodecagon C) heptagon D) hexagon E) decagon

16. Review 2 • Find m<A A) 65° B) 135° C) 100° D) 90° E) 105° B A 165° C 30° 65° D

17. Review 3 • Opposite angles of a parallelogram must be _______. A) complementary B) supplementary C) congruent D) A and C E) B and C

18. Review 4 • If a quadrilateral has four equal sides, then it must be a _______. A) rectangle B) square C) rhombus D) A and B E) B and C

19. Review 5 • ABCD is a trapezoid. Find the length of midsegment EF. A) 5 B) 11 C) 16 D) 8 E) 22 13 A E 11 B 5 D F C 9

20. Review 6 • The quadrilateral below is most specifically a __________. A) rhombus B) rectangle C) kite D) parallelogram E) trapezoid

21. Review 7 • PQRS is a rhombus. What is the value of b? Q 2b + 3 = 5b – 6 9 = 3b 3 = b P 2b + 3 R S 5b – 6

22. TEST- Polygons and Proof Do your best. Silence please. CORRECTION: For ADVANCED (A level) grade: Prove: Given ABCD is a Kite. Prove: ⦟BAE⦟BCE SHOW thinking, clearly and concisely, easy for Others to follow. FINISHED? You may work on the semester review packet.

23. practice • Do problems on your Semester 1 Review Sheet • Big Idea: Quadrilaterals • Big Idea: Proof • Big Idea: Triangle Properties

24. debrief What do you need to study to be ready for the final exam? How will you study so you will know them from vocabulary, properties and conjectures by memory? flip flops? 2 column practice? make up a practice quiz? other?