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1.find angles 1 and 2

Review. Put these questions on your half sheet of paper. 1.find angles 1 and 2. 2.find x. 3/4. find x in these two parallelograms. Rectangle. Definition - a parallelogram with four equal angles (i.e. right angles). Rectangle. Special characteristics of rectangles. Examples. Find x.

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1.find angles 1 and 2

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  1. Review Put these questions on your half sheet of paper 1.find angles 1 and 2 2.find x 3/4. find x in these two parallelograms

  2. Rectangle Definition- a parallelogram with four equal angles (i.e. right angles)

  3. Rectangle Special characteristics of rectangles

  4. Examples Find x A rectangle has four right angles, so, 3x-15 = 90 3x=105 x=35 3x-15 B A AT = 16, AC=6x+2, DT=5w-7 Find x and w T In a rectangle diagonals are bisected just like in any parallelogram, so AC=32 (twice AT), so 6x+2=32, solve and x=5 C D In a rectangle diagonals are equal so AC=BD and AT=DT so 5w-7 = 16, solve and w=23/5

  5. Practice Complete the following problems on your note sheet. A B AB = 6x-8 BT = 19 AC = 6y+2 CD = 22 T C D

  6. Practice cont. A B Complete the following problems on your note sheet. T C D A B T C D BT = 20 AC = w

  7. Rhombus Definition - a parallelogram with four equal sides

  8. Special characteristics of rhombuses

  9. Examples B AB= 5x-8, BC=6x-10 2 The diagonals of a rhombus are perpendicular so <1=90 Since a triangle sums to 180 the angle to the right of <2 is 57, and diagonals of a rhombus bisect the vertices so <2=57. Since a rhombus has 4 equal sides, AB=BC and 5x-8=6x-10, solve x=2 33 A C 1 D Find <1, <2, <3 Since a rhombus is a parallelogram, opposite angles are equal so <3=100 Also, consecutive angles add to 180 so the bottom left corner has to be 80. The diagonal bisects the corner <1 and <2 are equal, both are 40 100 2 3 1

  10. Practice W Complete the following problems on your note sheet. R H T W WR = 3x - 5 TR = x + 3 HT = 3y -2 R H T

  11. Practice cont. Complete the following problems on your note sheet. 70 <1=3x-1 <2=2x+7 Perimeter = 6w 15 1 2 Find angles 1-4

  12. Square - a parallelogram with four equal angles four equal sides - is both rectangle and rhombus - has all the characteristics of a rectangle and all the characteristics of a rhombus

  13. On a half piece of paper answer the following: Match the quadrilateral with the property: All sides equal A. Parallelogram All angles equal B. Rectangle Both diagonals equal C. Rhombus Opposite angles equal Diagonals are perpendicular Opposite sides equal Diagonals bisect vertices

  14. On a half piece of paper answer the following: Match the quadrilateral with the picture: A. Parallelogram B. Rectangle C. Rhombus D. Square 9 8 10 11 9 9 9 9

  15. On a half piece of paper answer the following: Find x, y, w, p in each figure. 12. Rectangle: AC = 30, BD= 6x – 6, AT = 4p-1 <1=3w, <2=4y-15, <3=40 A B T 1 D W C 2 3 R H 13. Rhombus: Perimeter = 80 <1 = 5x, <2=3w-8, WR=9p+8, RT=2y T 2 1 35

  16. THE END

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