1. Objectives: -Define quadrilateral, parallelogram, rhombus, rectangle, square, & trapezoid -Identify the properties of quadrilaterals and the relationship among the properties. Warm-Up: A new medical building containing 100 offices has just been completed. Richard was hired to paint the numbers 1 to 100 on the doors. How many times will Richard have to paint the number 9?

2. Quadrilateral: Any four sided polygon.

3. Trapezoid: A quadrilateral with one and only one pair of parallel sides.

4. Parallelogram: A quadrilateral with two pairs of parallel sides.

5. Rhombus: A quadrilateral with four congruent sides.

6. Rectangle: A quadrilateral with four right angles.

7. Square: A quadrilateral with four congruent sides and four right angles.

8. Euler Diagram (Venn Diagram): A diagram that is used to show logical relationships.

9. Kite: A figure with two pairs of congruent adjacent sides, and opposite sides that are not congruent.

10. Conjecture: Properties of Parallelograms Opposite sides of a parallelogram are: Opposite angles of a parallelogram are: Diagonals of a parallelogram: Consecutive angles of a parallelogram are:

11. Conjecture: Properties of Rhombuses A rhombus is a: The diagonals of a rhombus are:

12. Conjecture: Properties of Rectangles A rectangle is a: The diagonals of a rectangle are:

13. Conjecture: Properties of Squares A square is a:_______, ________, & _______ The diagonals of a square _________ each other, are ________, and are _________:

14. Example [parallelogram]: YZ = ___ XY = ___ WV = ___ VY = ___ m<WXY = ___ m<XWZ = ___ m<XYZ = ___ W X Y Z V

15. Example [rhombus]: GH = ___ HI = ___ FJ = ___ JH = ___ m<FIH = ___ m<GFI = ___ m<FJG = ___ m<HJI = ___ F J H G I J

16. Example [rectangle]: CD = ___ BC = ___ BD = ___ AE = ___ BE = ___ AC = 10 AD = 8 AB = 6 A B D E C E

17. Example [Square]: LM = ___ LN = ___ m<KOL = ___ m<LOM = ___ KL = 50 KM = 70.7 K N M E L O

19. Example: In rectangle WXYZ, diagonal WY = x+2 and diagonal XZ = 3x. Find x and the measure of the diagonals.