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A quadrilateral with both pairs of opposite sides parallel *opposite sides are congruent *opposite angles are congruent *diagonals bisect each other.

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Presentation on theme: "A quadrilateral with both pairs of opposite sides parallel *opposite sides are congruent *opposite angles are congruent *diagonals bisect each other."— Presentation transcript:

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2 A quadrilateral with both pairs of opposite sides parallel *opposite sides are congruent *opposite angles are congruent *diagonals bisect each other

3 Parallelogram with 4 congruent sides * all properties of parallelograms * Diagonals are * Diagonals Bisect each pair of opposite angles

4 A parallelogram with 4 right angles * All properties of Parallelograms *Diagonals are congruent

5 A parallelogram with 4 right angles and 4 congruent sides *All properties of parallelograms *All properties of Rhombuses *All properties of Rectangles

6 How do they fit together? Parallelogram Rhombus Rectangle Square When comparing top down, the shapes are sometimes. When comparing bottom up, the shapes are always

7 Example: decide if the statement is always, sometimes or never true. 1. A rectangle is a square1. Sometimes 2. A Square is a rhombus 3. A rhombus is a parallelogram 4. A square is a quadrilateral 5. A parallelogram is a rectangle 6. A square is a trapezoid 2. Always 3. Always 4. Always 5. Sometimes 6. Never

8 Example: ABCD is a rectangle. m

9 Example: ABCD is a rhombus. Find the value of x 140x A BC D

10 Example: ABCD is a rectangle. Find the value of x AB CD 7x-12 2x+13 7x-12 = 2x+13 5x-12=13 5x=25 x=5

11 Example: GHJK is a parallelogram Find A. JH =_______ B. LH = ______ K J H G 8 6 L 8 6

12 Example: in Parallelogram ABCD, m

13 Example: WXYZ is a parallelogram, find x W X Y Z 4x-9 3x+18 4x-9=3x+18 -3x X-9= X=27

14 Example: UVWX is a parallelogram U V W X Z 1. XU = 15, UW = 28, WZ= _____ 2.

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