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6.4 Properties of Special Parallelograms

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Presentation on theme: "6.4 Properties of Special Parallelograms"— Presentation transcript:

1 6.4 Properties of Special Parallelograms

2 Rectangles All rectangles are parallelograms- (all of the properties of parallelograms are the properties of rectangles) Opposite sides parallel Opposite sides congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other

3 Rectangles Other properties of rectangles
All angles are congruent (90o) Diagonals are congruent

4 Example 1) A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM.

5 Example 2) Carpentry The rectangular gate has diagonal braces. a) Find HJ. b) Find HK.

6 Rhombus All rhombi are parallelograms- (All the properties of parallelograms are the properties of rhombi) Opposite sides parallel Opposite sides congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other

7 Rhombus Other properties of rhombi All sides congruent
Diagonals are perpendicular Diagonals bisect opposite angles

8 Example 3) TVWX is a rhombus. a) Find TV. b) Find mVTZ.

9 Example 3) CDFG is a rhombus. a) Find CD. b) Find mGCH if mGCD = (b + 3)° and mCDF = (6b – 40)°

10 Square All squares are parallelograms (so squares have all parallelogram properties) Opposite sides parallel Opposite sides congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other

11 Square All squares are rectangles (so squares have rectangle properties) All angles are congruent Diagonal are congruent All squares are rhombi (so squares have rhombi properties) All sides congruent Diagonals are perpendicular Diagonals bisect opposite angles

12 Example KHIJ is a square. Find x. IJ=6-3x Perimeter=112 cm I H K J

13 Example KHIJ is a square. Find x. mHIL=2x+15 I H L L K J

14 Example Determine if each set of vertices form a parallelogram, rectangle, rhombus, or a square. List all that apply. A(5, 2) B(1, 9) C(-3, 2) D(1, -5) A(1, 1) B(-2, 4) C(-5, 1) D(-2, -2) A(-4, 0) B(3, 7) C(6, 4) D(-1, -3)


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