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)