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Updated on Oct 5, 2011

Review the following concept if necessary: Quadrilaterals Study Guide.

### Problems

Use the diagram to determine whether each statement is true or false.

2. All parallelograms are rectangles.
4. All parallelograms are squares.
5. All squares are both rectangles and rhombuses.
6. All rectangles are both parallelograms and quadrilaterals.
7. All rhombuses are squares.
8. All isosceles trapezoids are parallelograms.
9. All squares are trapezoids.

Use the following figure of parallelogram ABCD to answer questions 11– 15.

1. BC
2. DC
3. mB
4. mA
5. mD

Use the following figure of parallelogram PQRS to answer questions 16– 20.

1. SQ
2. OR
3. mPQR
4. mSPQ
5. mSRQ

Use the following figure to find the side length and angle measures for rectangle PQRS for questions 21–24.

1. QS
2. OP
3. mQSR
4. mRPS

Use the Pythagorean theorem to solve questions 25 and 26.

1. Find PQ, given OR = 5 and QR = 6.
2. Determine the perimeter of rectangle PQRS.

Use the following figure to find the angle measures for rhombus GHJK for questions 27–32.

1. mHGK
2. mGHJ
3. mJMK
4. mGJK
5. mHJK
6. mGKH

1. Explain how this Venn diagram and the flowchart shown at the beginning of this lesson show the relationships among quadrilaterals.

1. true
2. false
3. true
4. false
5. true
6. true
7. false
8. false
9. false
10. false
11. 8
12. 12
13. 65°
14. 115°
15. 65°
16. 14
17. 5
18. 55°
19. 125°
20. 125°
21. 30
22. 15
23. 25°
24. 65°
25. 8
26. 28
27. 58°
28. 64°
29. 90°
30. 58°
31. 116°
32. 32°
33. Parallelograms and trapezoids are both quadrilaterals, but a trapezoid can never be a parallelogram or vice versa. Rhombuses and rectangles are parallelograms, with squares being both rhombuses and rectangles. Isosceles trapezoids are a special type of trapezoid.

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