1. 6-4 Properties of Special Parallelograms
Geometry

2. Special Parallelograms
Rhombus- a ||’ogram with sides
Rectangle- a ||’ogram with 4 rt s.
Square- a ||’ogram with sides and 4 rt s

3. So far: (we’ll add more later)_
Quadrilaterals _
parallelograms _ _
rhombus _
rectangle
square

4. Corollaries
Rhombus corollary- a quad is a rhombus iff it has sides.
Rectangle corollary- a quad is a rectangle iff it has 4 rt ‘s
Square corollary- a quad is a square iff it is a rhombus and a rectangle.

5. Ex. 1 sometimes, always, never?
A rhombus is a square.
A parallelogram is a rectangle.
A square is a regular quadrilateral.
A rectangle is a quadrilateral.
Sometimes
Sometimes, if is has 4 rt ‘s
Always

6. Properties of Rectangles 6-4-1
If a quadrilateral is a rectangle, then it is a parallelogram.
B C
ABCD is a
parallelogram.
A D

7. Properties of Rectangles Thm 6-4-2
A ||’ogram is a rectangle iff its diagonals Q R
If QRST is a rectangle then
If then QRST is a rectangle. T S

8. Ex. 2
A woodworker constructs a rectangular picture frame so that JK = 50 cm & JL = 86 cm. Find HM.
K L H
J M
½ of 86 = 43 cm = HM

9. Properties of Rhombuses 6-4-3
If a quadrilateral is a rhombus, then it is a parallelogram B C
ABCD is a parallelogram
A D

10. Properties of Rhombuses Thm 6-4-4
A parallelogram is a rhombus then its diagonals are . J K
If , then JKLM is a rhombus.
If JKLM is a rhombus, then __ __ M L

11. Properties of Rhombuses Thm 6-4-5
A ||ogram is a rhombus iff each diagonal bisects a pair of opposite s. B A (( ) (( ) )) )) ( ( D C

12. Ex. 3
A)TV= 7.9
B) 20°

13. Ex. 4
Show that diagonals of square EFGH are congruent perpendicular bisectors of each other. E(-4,-1), F(-1,3), G(3,0), H(0,-4).
1) graph
2) Show diagonals are congruent using distance formula for diagonals
3) Show slope of diagonals (which should be opposite & reciprocals of each other)
4) Show midpoint of both diagonals which should be the same order pair.
Distance , slope & midpt formula

14. Graph for Ex. 4 1.) graph

15. 2.) 3.) 4.)

16. Assignment