Kites Another Type of Quadrilateral. Review of Quadrilaterals ParallelogramHas two parallel pairs of opposite sides. RectangleHas two pairs of opposite.

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Presentation transcript:

Kites Another Type of Quadrilateral

Review of Quadrilaterals ParallelogramHas two parallel pairs of opposite sides. RectangleHas two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. SquareHas two pairs of parallel sides, four right angles, and all four sides are equal. It is also a rectangle and a parallelogram. RhombusA parallelogram with four equal sides. Not a square because it does not have four right angles.

Trapezoids and Kites  A Trapezoid is a quadrilateral because it has four sides. It is NOT a parallelogram because both pairs of opposite sides are not parallel.  Another type of quadrilateral that is NOT a parallelogram is a Kite.  Definition of a Kite:  Kite – A quadrilateral with two pairs of congruent, adjacent sides.

Properties of a Kite  The diagonals of a kite are perpendicular. The longer diagonal is the bisector of the shorter diagonal.  There is exactly one pair of opposite angles that are congruent.  There are two consecutive pairs of congruent sides.

Examples of Kite Properties Diagonals are Perpendicular One pair of opposite angles are congruent Two consecutive, adjacent pairs of congruent sides

Example #1  Given: GJIH is a Kite. HG=HI and IJ=GJ. The following questions are true or false.  True False True False

Example #2  Given: GJIH is a Kite. HI = 10, GJ = 18. IK = 8 and KG = 8. Find the following values:  HG =  IJ =  IG =  HK =  KJ =  HJ =

Example #3  Given: WXYZ is a Kite. WX = YX and WZ=YZ. Find the following angles:  VYZ =  VXY =  WZY =  XWZ =  WXY =