Download 6.4/6.6 Worksheet #1 Name: Geometry Hour: _____ Definition: A

6.4/6.6 Worksheet #1
Geometry
Name: ______________________
Hour: _____
Definition: A rhombus is a quadrilateral with four _________________ sides.
Because a rhombus is a parallelogram…
1. The opposite sides of a rhombus are _________________________
2. The opposite angles of a rhombus are ________________________
3. The consecutive angles of a rhombus are _____________________
4. The diagonals of a rhombus __________________ each other.
In addition, the rhombus has two special properties:
5. The diagonals of a rhombus are __________________________
6. The diagonals of a rhombus __________________ the corner angles.
Answer the following as true or false.
_____ 7. Every rhombus has to be a parallelogram.
_____ 8. Every parallelogram has to be a rhombus.
_____ 9. The consecutive angles of any rhombus are complementary.
_____ 10. The opposite angles of any rhombus are congruent.
_____ 11. The opposite sides of a rhombus are parallel and congruent.
13. Which word is MORE descriptive – parallelogram or rhombus? Explain your answer.
14. Is a parallelogram a special kind of rhombus or is a rhombus a special kind of parallelogram?
Judging by the markings on the picture and what you know about the properties of parallelograms
and rhombuses, state whether each shape is a parallelogram or a rhombus.
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Use the diagrams to answer the questions.
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DE = ____ EF = ____ GF = _____
Equation:
Equation:
x = ___________
x = ___________
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x = _______
x = _________
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28.
Fill in ALL missing angles of each shape. #29-31 are parallelograms and #32-33 are rhombuses.
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Using the properties of rhombuses, write and solve an algebraic equation for each picture.
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Equation:
Equation:
Equation:
x = _________
x = _________
x = __________
Using the properties of each shape to write and solve an algebraic equation for each picture.
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Equation:
Equation:
x = _____ m∠ABC = _____ m∠BCD = _____
x = _____
40. In a rhombus ABCK, AB = 7x – 3 and CD = 25. What is the value of x.
A. 3
B. 7
C. 4
D. 25
41. STUV is a rhombus. What are the values of x and y?
A. x = 3, y = 3
B. x = 6, y = 3
C. x = 3, y = 8
D. x = 6, y = 4
42. The diagonals of a parallelogram _______?
A. are congruent
B. are perpendicular
C. bisect each other
43. KLMN is a parallelogram. Which of the following statements is false?
A. KP = MP
B. LP = NP
C. LM = KN
D. LN = KM
D. are parallel
M
True or False. If False, give a reason/counterexample why.
44. Every rhombus is a parallelogram. ________________________________________
45 The diagonals of a rhombus bisect each other. ________________________________________
46. The diagonals of any rhombus are congruent. ________________________________________
47. Opposite ANGLES of a parallelogram are congruent. ________________________________________
48. The consecutive SIDES of a rhombus are congruent. ________________________________________
Find the measure of each angle or length of each segment.
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