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Chapter 6 – Quadrilaterals

Chapter 6 – Quadrilaterals. In this chapter you will learn about the special properties of quadrilaterals as well as find their perimeters and areas. You will explore the relationships of the sides and diagonals of a parallelogram, kite, trapezoid, rectangle, and rhombus. . 6.1.

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Chapter 6 – Quadrilaterals

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  1. Chapter 6 – Quadrilaterals In this chapter you will learn about the special properties of quadrilaterals as well as find their perimeters and areas. You will explore the relationships of the sides and diagonals of a parallelogram, kite, trapezoid, rectangle, and rhombus.

  2. 6.1 What If Both Sides Are Parallel? Pg. 4 Parallelograms

  3. 6.1 – What If Both Sides are Parallel?_____ Parallelograms In the past, you used your knowledge to find the area of squares and rectangles. But what if the shape didn't have right angles?

  4. 6.1 –PARALLELOGRAMS Find the areas of the figures below. Can you find more than one method for finding the area?

  5. 2 4 2 8 un2

  6. 4 12 20 un2 4

  7. 6.2 –AREA OF A PARALLELOGRAM A parallelogram: a four-sided shape with two pairs of parallel sides. How can you find the area of a parallelogram? Consider this question as you answer the questions below.

  8. a. Keesha thinks that the rectangle and parallelograms below have the same area. Her teammate Saundra disagrees. Who is correct? Justify your conclusion.

  9. 15 un2 15 un2 15 un2

  10. Area of Parallelogram

  11. b. Does the angle at which the parallelogram slants matter? Why or why not? Explain how you know. No, the base is the same and the height is always perpendicular

  12. Parallelogram A = bh

  13. 6.3 – AREA OF PARALLELOGRAMS, CONT. Several more parallelograms are shown below. In each case, find a related rectangle for which you know both the base and height. Rotating your packet might help. Use what you know about rectangles to find the area of each parallelogram.

  14. A = bh A = (9)(4) A = 36un2

  15. A = bh A = (20)(5) A = 100un2

  16. A = bh A = (7)(3) A = 21un2

  17. Definition: If a quadrilateral is a parallelogram, then both pairs of ________________ sides are ______________. opposite parallel

  18. If a quadrilateral is a parallelogram, then both pairs of ________________ sides are ______________. opposite congruent

  19. If a quadrilateral is a parallelogram, then both pairs of ________________ angles are ________________. opposite congruent

  20. If a quadrilateral is a parallelogram, then both pairs of _______________ angles are ___________________. consecutive supplementary x y y x

  21. If a quadrilateral is a parallelogram, then the diagonals _______________ each other. bisect

  22. 6.5 –PARALLELOGRAM PARTS Find the value of each variable in the parallelogram.

  23. a – 3 = 14 a = 17 b + 2 = 7 b = 5

  24. 3x + 6 = 12 3x = 6 x = 2 2y + 9 = 27 2y = 18 y = 9

  25. 130° 50° 50°

  26. 7a – 3 + 106 = 180 9b – 2 = 106 7a + 103 = 180 9b = 108 7a = 77 b= 12 a = 11

  27. congruent parallelogram

  28. congruent parallelogram

  29. supplementary parallelogram

  30. bisect parallelogram

  31. New!!! congruent parallel parallelogram

  32. 6.6 –PROVING PARALLELOGRAMS Can you prove the quadrilaterals are parallelograms? Why or why not?

  33. yes yes Both pairs of opposite angles are congruent One pair of opposite sides parallel and congruent

  34. yes no Both pairs of opposite sides are congruent Parallel and congruent marks are not on the same sides.

  35. no yes Only one pair of congruent angles Both pairs of opposite sides are parallel

  36. yes Diagonals bisect each other

  37. 6.7 –PARALLELOGRAM IDENTIFICATION The definition of a parallelogram is, "A quadrilateral with both opposite sides parallel." Based on this definition, circle all parallelograms below.

  38. a. What is the slopes of all four line segments? 2 7 8 1 B AB = ______BC = ______ CD= ______AD = ______ 7 A 2 8 1 2 7 8 1 C D

  39. b. What is the relationship between these sides, given the slopes? Explain. 2 7 8 1 B AB = ______BC = ______ CD= ______AD = ______ 7 A 2 A 8 1 2 7 8 1 Both opposite sides are parallel C D

  40. c. What is the length of all four line segments? B AB = ______BC = ______ CD= ______AD = ______ 7 A 2 A 22 + 72 = d2 12 + 82 = d2 4 + 49 = d2 1 + 64 = d2 8 53 = d2 65 = d2 1 C D

  41. d. What is the relationship between these sides, given their length? Explain. B AB = ______BC = ______ CD= ______AD = ______ 7 A 2 A 8 Both opposite sides are congruent 1 C D

  42. e. What kind of quadrilateral is this? How do you know? Parallelogram, Both opposite sides are parallel and congruent B 7 A 2 A 8 1 C D

  43. Parallelogram Trapezoid Isosceles Trapezoid Rectangle Rhombus Kite Square Triangle

  44. Name Block #

  45. Parallelogram

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