Name ___________________________________________ Date _____________________ Class ____________________
6.4 & 6.5 Special Parallelograms
Unit 6: Polygons & Quadrilaterals
For each property listed, place an “X” in the box for the quadrilaterals that have that
property. There may be more than one quadrilateral for each property.
Parallelogram
Property
Rectangle
Rhombus
Square
Same-side angles supplementary
Angles are all right angles
Opposite angles congruent
Diagonals bisect each angle
Diagonals bisect one another
Congruent diagonals
All sides congruent
Diagonals perpendicular
Opposite sides parallel
Match each figure with the letter of one of the vocabulary terms. Use each term once.
1.
2.
_____________________
3.
____________________
A. rectangle
B. rhombus
C. square
____________________
Fill in the blanks to complete each statement.
4. If a parallelogram is a rhombus, then its diagonals are ___________________.
5. If a parallelogram is a rectangle, then its diagonals are ___________________.
6. If a quadrilateral is a rectangle, then it is a ___________________.
7. If a parallelogram is a rhombus, then each diagonal ___________________
a pair of opposite angles.
8. If a quadrilateral is a rhombus, then it is a ___________________.
Tell whether each figure must be a rectangle, rhombus, or square based on the information
given in the diagram. Use the most specific name possible.
9.
10.
___________________________
11.
___________________________
___________________________
This graphic organizer shows that each inside shape contains all the properties of
the boxes surrounding it. For example, the shape with “squares” is inside the other
shapes. Thus, a square “contains” all the properties of rectangles, rhombuses, parallelograms,
and quadrilaterals.
A quadrilateral is a
polygon with 4 sides.
A parallelogram is a
quadrilateral with 2
pairs of parallel sides. It
has other properties.
A rectangle is a
parallelogram with 4 right
angles. It has other
properties and “contains”
the properties of a
parallelogram.
A rhombus is a parallelogram
with 4 congruent sides. It has
other properties and
“contains” the properties of a
parallelogram.
A square “contains” properties of a
rhombus, a rectangle, a
parallelogram, and a quadrilateral.
Use the graphic organizer above to answer the following.
12. Is a triangle a quadrilateral?
____________________
13. Is a square a rectangle?
____________________
14. Is a rhombus always a parallelogram?
____________________
15. Is a rectangle always a rhombus?
____________________
16. Is a quadrilateral always a parallelogram?
____________________
17. What do all quadrilaterals have in common?
_________________________________________________________________________________________________
18. What would you have to change in a rhombus to make it a square?
_________________________________________________________________________________________________
19. What would you have to change in a rectangle to make it a square?
_________________________________________________________________________________________________
20. Complete the table below:
If the Diagonals are . . .
congruent
perpendicular
congruent and perpendicular
. . . then the Parallelogram is a
A modern artist’s sculpture has rectangular faces. The face shown
here is 9 feet long and 4 feet wide. Find each measure rounded to the
nearest tenth. (Hint: You will need to use the Pythagorean Theorem.)
21. DC
_____________________
22. AD
_____________________
23. DB
_____________________
24. AE
_____________________
The part of a ruler shown is a rectangle
1
with AB 3 inches and BD 3 inches.
4
Find each length.
9. DC
_________________________
10. AC
_________________________
ABCD is a rectangle. Find each length.
25. BD
___________________________
27. AC
___________________________
26. CD
___________________________
28. AE
___________________________
GOAT is a rhombus with m OGT = 70°. Find each measure
29. m OAT
___________________________
31. m GOA
___________________________
33. m OXA
___________________________
30. m OAX
___________________________
32. m GOX
___________________________
34. m OTA
___________________________
COAL is a square with LC = 4. Find each measure
35. AO
___________________________
37. CA
___________________________
39. m CLA
___________________________
36. CO
___________________________
38. CS
___________________________
40. m OAS
___________________________
KLMN is a rhombus. Find each measure.
41. KL
___________________________
42. m MNK
___________________________
MNOP is a square. Find each measure.
43. m MNO
___________________________
44. MP
___________________________
WXYZ is a rectangle. Find each measure.
45. m ZYX
___________________________
46. XY
___________________________
DEFG is a rhombus. Find each measure.
47. m DGF
___________________________
48. m EDG
___________________________