1. Geometry 10 December 2012 1) Place your book and binder on your desk. 2) Put papers from folder into in your binder. 3) WARM UP a) Do proof “strip” b) Do Investigation 1, page 275 - draw a triangle on patty paper - pinch each side to find midpoints - draw mid-segments - copy one small triangle on 2 nd patty paper - compare triangles

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. due Tuesday 5.4: 2, 3, 4, 7 5.5: 1, 2, 3, 5, 6 5.6: 11, 12, 13 TEST- proofs, polygon properties Wednesday/ Thursday Semester Review Packet due on your final exam day P2- Monday, December 17 P3- Tuesday, December 18 P5 and P6- Wednesday, December 19

4. Kite Properties

5. Isosceles Trapezoids

6. PQRS is an isosceles trapezoid. Find m<P, m<Q, and m<R. SR P Q 50° > > m<R= 50 ⁰ m<Q= m<P= 180 – 50 = 130º check: 2(50) + 2(130) = 100 + 260 = 360√ base angles are congruent consecutive angles are supplementary

7. A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle

8. Triangle Midsegments Continue with investigation 1…. - compare angles what can you conclude about the mid-segment and the third side? - compare length of mid-segment with the length of the 3 rd side what can you conclude?

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

10. Mid-segments of a trapezoid Watch video: http://www.youtube.com/watch?v=O2bf1mZQ WXI http://math.kendallhunt.com/x19429.html Shope Demo with Patty Paper Trapezoids

11. Midsegment of a trapezoid The midsegment of a trapezoid is the segment that connects the midpoints of its legs.

12. Midsegment of a trapezoid parallel to each baseits length is one half the sums of the lengths of the bases. The midsegment of a trapezoid is parallel to each base and its length is one half the sums of the lengths of the bases. MN ║AD, MN║BC MN = ½ (AD + BC)

13. Ex. 3: Finding Midsegment lengths of trapezoids LAYER CAKE A baker is making a cake like the one at the right. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer be?

14. Use the midsegment theorem for trapezoids. DG = ½(EF + CH)= ½ (8 + 20) = 14” C D E D G F

15. Parallelogram Properties http://math.kendallhunt.com/x19430.html http://www.mathwarehouse.com/geometry/quadrilate rals/parallelograms/#anglesParallelogram http://www.youtube.com/watch?v=ioTBllxJ91s

16. 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

17. Using Properties of Parallelograms PQRS is a parallelogram. Find the angle measure.  m< R  m< Q Q R SP 70° =70 ° 70 ° + m < Q = 180 ° m< Q = 110 °

18. Debrief What did you learn today? What will you do to be ready to do your best on the final exam?