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Objectives : -Define quadrilateral, parallelogram, rhombus, rectangle, square, & trapezoid

3.2 Properties of Quadrilaterals. Objectives : -Define quadrilateral, parallelogram, rhombus, rectangle, square, & trapezoid -Identify the properties of quadrilaterals and the relationship among the properties. Warm-Up:

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Objectives : -Define quadrilateral, parallelogram, rhombus, rectangle, square, & trapezoid

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  1. 3.2 Properties of Quadrilaterals 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 V Z Y m<WZY = WY = 13 WX = 10 WZ = 4

  15. Example [rhombus]: GH = ___ HI = ___ FJ = ___ JH = ___ m<FIH = ___ m<GFI = ___ m<FJG = ___ m<HJI = ___ F J J I G H m<FGH = FH = 15 FG = 21

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

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

  18. Example: In a parallelogram PQRS m<P=and m<Q=. Find x and the measure of each angle in PQRS.

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

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