1. Bellwork  Solve for x 5x+3 3x+1 26 No Clickers

2. Bellwork Solution  Solve for x 5x+3 3x+1 26

3. Section 8.6

5. The Concept  Today we’re going to be looking at the whole of our quadrilaterals to help delineate between them  This process will aid in our understanding of the nuances between all three of them

6. The Dreaded Graphic Organizer  Yesterday we talked about how quadrilaterals are grouped…we found them to look like… Quadrilaterals Parallelograms Rhombuses Rectangles Squares Kites Trapezoids Isosceles Trapezoids Right Trapezoids

7. Based on our picture Which quadrilaterals 1. Have at least one pair of congruent sides? 2. Have diagonals that are perpendicular 3.Are equilateral and equiangular 4.Have congruent consecutive angles 5.Have four sides 6.Has congruent diagonals 7.Has diagonals that bisect each other Quadrilaterals Parallelograms Rhombuses Rectangles Squares Kites Trapezoids Isosceles Trapezoids Right Trapezoids

8. Naming Knowing the various properties of a quadrilateral is invaluable when faced with the task of identifying or naming a quadrilateral For example: What is the name of this object?

9. Naming What is the name of this object?

10. Naming What is the name of this object? Because we don’t know if these are right angles, we cannot call it a rectangle

11. Naming What is the name of this object? Both a Rhombus and a Kite have perpendicular diagonals, but we don’t know anything else about this object

12. Naming Do we have enough information to say that this object is a Rhombus? 55 o 15 125 o 55 o

13. Homework  8.6 13-16, 18-20, 23, 26-28, 36

14. Practical Example What quadrilateral is shown below 56 o 24”

15. Practical Example Explain why a parallelogram with one right angle must be a rectangle?

16. Most Important Points  Delineation of properties of quadrilaterals  Using properties to name objects

17. Question Practice  Four limbs  Eyes on the side of their head  Large ears  Quadripodal motion  A mostly vegetarian diet  Large Feet that also aid in swimming  Very wrinkled rough skin  An extended large snout

18. Question #1  A set of congruent opposite angles  Bisected Diagonals  No right angles  Perpendicular Diagonals  Equilateral

19. Question #2  A set of sides of equal length  Diagonals that serve as angle bisectors  Supplementary consecutive angles  Two sets of parallel sides  Congruent diagonals

20. Question #3  Two short sides and two long sides  A set of congruent opposite angles  A set of sides of equal length  Perpendicular diagonals  No sides parallel

21. Question #4  Two short sides and two long sides  Two sets of supplementary consecutive angles  A set of parallel sides  A 90 o angle  Not equilateral  Not equiangular