| Review 5.4-6 | Name______________________________________ | ||
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1. Draw a concave quadrilateral.
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2. How many sides does a polygon with 65 diagonals have?
13 |
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3.. Know
the properties of Parallelograms, Rectangles, Rhombuses, Squares, Kites
, Trapezoids, Isosceles Trap. Write the name of every special quadrilateral which has the given property |
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| a) Both pairs of opposite sides parallel. Parallelogram, Rectangle, Rhombus and Square | |||
| b) Exactly one pair of opposite sides are parallel Trapezoid and Isosceles Trapezoid | |||
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Each diagonal bisect the corner angles from which it is drawn Rhombus and Square |
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| d) Diagonals are perpendicular. Rhombus Square and Kite | |||
| e) Diagonals are perpendicular bisectors of each other. Rhombus and Square | |||
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4. Find measures of angles if given the type of quadrilateral.
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| <1 and <2 = 45, <3 = 90 | <1 = 56,<2=34, and <3 = 90 | <1 = 24, <2 = 66, If you have to find an angle where the diagonals intersect, subtract the two angles of the triangle from 180 to find the last angle. | |
| Use parallelogram ACFG to answer the questions below |  |
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| 5. If AX = 4m+2 and XC = 3m - 1, and XF = 2m + 8, find GC. | AX = XF, 4m + 2 = 2m+8, m= 3, XC = 3m-1 or 3(3)-1=8 so GC = 16 | ||
| 6. If m <CAF = 5a+20 and m <AFG = 50, and m<GAF = 2a + 10, find m<ACF | <CAF = <AFG, 5a+20 = 50, a = 6, <GAF= 2(6)+10 =22, < GAC = 50 +22= 72, m<ACF = 108 | ||
| 7. If AX = XC, AX = 4t + 10 and XC = t + 16, find AF | 4t+10=t+16, t=2, AX = 18, AF= 36 | ||
| 8. If < AGF = 5x+6 and < ACF = 7x - 4, find the measure of < GAC | 5x+6=7x-4, x=5, <AGF = 31, <GAC = 149 (suppl) | ||
| 9. The coordinates of the vertices of quadrilateral MPZQ are M(-2,-1), P(2,5), Z (3,1), and Q(-1,-5). Is the quadrilateral a parallelogram. How could you test to see if it was a rhombus? Opposite sides have the same slope so it is a parallelogram, to test for a rhombus make sure diagonals are also perpendicular ( neg reciprocal slopes) | |||
| 10. If CDMN is an isosceles trapezoid. If CM = 12 , ND =
2x+6 and CN = 3x, find DM.
2x+6=12, x=3 CN=DM= 3(3)=9 |
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| 11. FISH is a rhombus with FI = 6x+2, and SI = 8x-4. Find the perimeter of FISH. | FI = SI, 6x+2=8x-4, x=3, sides are each 20, perimeter = 80 | ||
| Given: Quadrilateral MNPQ answer the following questions. |  |
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| 12. If MR = PR and ___?___
then MNPQ is a parallelogram by what reason? QR =
RN Diagonals bisect each other 13. If MQ // NP and __?___ then MNPQ is a parallelogram by what reason? QP// MN Def of Parallelogram or MQ= NP One pair of sides both congruent and parallel (OPCP) |
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| 14. If WXYZ is a rhombus and m<WXY = 118, then m<ZWY <ZWX is the supplement or 62, <ZWY is half as the diagonals bisect the corner angles - Answer is 31 |  |
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| If it is possible to prove the quadrilateral is a parallelogram from the given information, name the parallelogram and state the principal definition or theorem that allows you to conclude this. If it is not possible write none. |  |
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| 15. FG = BG, AG = EG | FEBA is a Parallelogram Diagonals bisect each other | ||
| 16. <BED = <C, < EBC = <D | BEDC is a parallelogram - Both pair of opposite angles are congruent | ||
| 17. FE = AB, FA // EB | Can't be proven - None | ||
| 18. FA=EB, FA // EB | FABE - one pair of sides are both congruent and parallel OPCP | ||
| Be able to
do a crook problem
Draw in parallel line and find the
alternate interior angles |
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| Be able to tell what kind of
quadrilateral is formed given certain directions.
If you join the midpoints of the sides of any quadrilateral, what type of quadrilateral is formed.
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