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Problem Set

Kite Trivia - In 1901, Gugliemo Marconi, inventor of the wireless telegraph, used a kite to loft an antenna four hundred feet in order to receive the first radio signal ever transmitted across the ocean.
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A kite is a special quadrilateral, but it is not a parallelogram or a trapezoid. A quadrilateral is a kite if and only if it has exactly two distinct pairs of congruent consecutive sides and its diagonals intersect.   Since a kite is not a parallelogram or a trapezoid, we cannot assume that it has any of the same characteristics as these quadrilaterals. The characteristics of a kite must be discovered and then proven.

Part I: Determine if a kite has any of the following characteristics. Write yes or no. (1/2 point each)

  1. Both pairs of opposite sides are parallel.
  2. Both pairs of opposite sides are congruent.
  3. The diagonals bisect each other.
  4. One diagonal bisects the other diagonal.
  5. The diagonals are congruent.
  6. Each diagonal bisects a pair of opposite angles.
  7. One diagonal bisects a pair of opposite angles.
  8. The diagonals are perpendicular.
  9. Both pairs of opposite angles are congruent.
  10. One pair of opposite angles are congruent.

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Part II. (1 point each)

1.    In kite ABCD, AB = BC and CD = DA. If AB = (3x - 4), BC = x + 8, CD = y + 7, and DA = 2y + 5, find the perimeter of the kite.

2.    Draw a Venn Diagram illustrating the positions of the following quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid,
        and kite. You may use a drawing program ie. Kidpix or you may make your own diagram.

3.    Describe (visually) the similarities and differences between each of the following quadrilaterals and kites: parallelograms, rectangles,
        rhombuses, squares, and trapezoids.  Be creative with this problem.

4.    A kite is tethered to a stake in the ground by a string 40 ft. long, which makes an angle of 60 degrees with the ground. How high is the kite?

5.    In problem number 6, if the kite fell vertically to the ground, how far away from the stake would the kite land?

6.    A kite flying 20 ft. above the ground is attached to a string 80 ft. long. The string is being held by a person on the ground. Find the angle
        between the string and the ground.

7.    A kite flying 30 ft. above the ground is attached to a string which makes a 52 degree angle with the ground. Find the length of the string.





Kite Trivia - In 1847, a suspension bridge was built across the Niagara River with the aid of a kite. When Chief Engineer T.G. Hulett was unable to carry the first steel cables across the mighty Niagara Gorge, he decided that a kite might solve his problem. A kite-flying contest was held and Hulett offered ten dollars to anyone who could fly a kite line to the other side of the river. Only one flyer was successful - a determined young boy named Homan Walsh. When Walsh's kite landed on the opposite shore, the flying line was then tied to stronger lines, which were used to pull the cables in place.

 

 

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