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Quadrilaterals: Properties and Relationships

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Learn about parallelograms, trapezoids, and quadrilaterals, their definitions, properties, and important formulas. Explore the sum of interior angles, types of parallelograms, diagonal properties, and solving geometric problems.

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Quadrilaterals: Properties and Relationships

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  1. Always Sometimes Never Parallelograms Definitions Trapezoids Quadrilaterals 1 pt 1 pt 1 pt 1 pt 1 pt 2 pt 2 pt 2 pt 2 pt 2 pt 3 pt 3 pt 3 pt 3 pt 3 pt 4 pt 4 pt 4 pt 4 pt 4 pt 5 pt 5 pt 5 pt 5 pt 5 pt

  2. 1 pt What is the sum of the interior angles of a quadrilateral?

  3. 1 pt Answer: 360 Degrees

  4. 2 pt What is true about consecutive angles of a rhombus?

  5. 2 pt Answer: They are SUPPLEMENTARY

  6. 3 pt What is the equation used to find the length of a median of a trapezoid?

  7. 3 pt Answer:

  8. 4 pt What is a quadrilateral called with congruent diagonals that are not perpendicular?

  9. 4 pt Answer: RECTANGLE

  10. 5 pt What is a quadrilateral called with diagonals that are angle bisectors but they are not congruent?

  11. 5 pt Answer: A Rhombus

  12. 1 pt What are four of the five properties of a parallelogram?

  13. 1 pt • Answer: • Opposite sides are parallel • Opposite sides are congruent • Opposite angles are congruent • Diagonals bisect one another • Consecutive angles are supplementary

  14. 2 pt What type of parallelogram ALWAYS has the following property? (you may have more than one answer) Diagonals bisect each other

  15. 2 pt Answer: Parallelogram, Rectangle, Rhombus, and Square

  16. 3 pt The perimeter of a rectangle is 40cm. The length is 4cm longer than the width. What are the measures of the length and the width?

  17. 3 pt Answer: Width=8cm Length=12cm

  18. 4 pt What is the length of the diagonal of a square who’s area is 100 square inches?

  19. 4 pt Answer: inches or 14.14 inches

  20. 5 pt The perimeter of the rhombus is 128 inches. One diagonal is 30 inches. Find the length of the other diagonal.

  21. 5 pt Answer: Approx. 56.6 inches

  22. 1 pt How is a rhombus different from a parallelogram?

  23. 1 pt Answer: A rhombus always has four congruent sides. And, its diagonals are perpendicular to each other and they are angle bisectors.

  24. 2 pt Can a rectangle ever be a rhombus? Why or why not?

  25. 2 pt Answer: Yes because a SQUARE has the properties of both a rectangle and a rhombus.

  26. 3 pt What makes a trapezoid different from a parallelogram?

  27. 3 pt Answer: A trapezoid has only one set of parallel sides.

  28. 4 pt What type of quadrilaterals will always have congruent diagonals?

  29. 4 pt Answer: Rectangles and squares

  30. 5 pt The vertices of a quadrilateral are located at (10,4), (10,8), (-4,8), and (-4,4) in this order. Is this a parallelogram, rectangle, rhombus, or a square? Please be as specific as possible.

  31. 5 pt Answer: It is a parallelogram and a rectangle

  32. 1 pt What is true about the angles in a trapezoid that share a leg?

  33. 1 pt Answer: They are supplementary

  34. 2 pt What are the congruent sides called in an isosceles trapezoid?

  35. 2 pt Answer: Legs

  36. 3 pt One of the bases of a trapezoid is 15ft long. The other base is 28ft long. How long is the median?

  37. 3 pt Answer: 21.5 ft

  38. 4 pt The median of a trapezoid is 31 inches long. One of the bases is 17 inches long. How long is the other base?

  39. 4 pt Answer: 45inches

  40. 5 pt ABCD is a trapezoid with a median EX. EX=x+5 and CD+AB=4x+6. How long is the median?

  41. 5 pt Answer: 7

  42. 1 pt A square is a parallelogram.

  43. 1 pt Answer: ALWAYS

  44. 2 pt Consecutive angles of a rectangle are supplementary.

  45. 2 pt Answer: ALWAYS

  46. 3 pt The diagonals of a rectangle are angle bisectors.

  47. 3 pt Answer: SOMETIMES

  48. 4 pt A quadrilateral has only two right angles.

  49. 4 pt Answer: SOMETIMES

  50. 5 pt A rhombus has consecutive sides that are perpendicular.

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