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1. 1. Quadrilaterals Project By Kayti Rose
2. 2. Properties of ParallelogramsThe opposite sides are parallel by definition.The opposite sides are congruent.The opposite angles are congruent.The diagonals bisect each other.Any pair of consecutive angles are supplementary.Each diagonal separates it into two congruent triangles.
3. 3. Properties of RectangleAll the properties of a parallelogram apply by definition.All angles are right angles.The diagonals are congruent.
4. 4. Properties of KitesTwo distinct pairs of adjacent sides are congruent by definition.The diagonals are perpendicular.One diagonal is the perpendicular bisector of the other.One of the diagonals bisects a pair of opposite angles.One pair of opposite angles are congruent.
5. 5. Properties of RhombusesAll the properties of a parallelogram apply by definition.Two consecutive sides are congruent by definition.All sides are congruent.The diagonals bisect the angles.The diagonals are perpendicular bisector of each other.The diagonals divide the rhombus into four congruent righttriangles.
6. 6. Properties of SquaresAll the properties of a rectangle apply by definition.All the properties of a rhombus apply by definition.The diagonals form four congruent isosceles right triangles.
7. 7. Properties of Isosceles TrapezoidsThe legs are congruent by definition.The bases are parallel by definition.The lower base angles are congruent.The upper base angles are congruent.The diagonals are congruent.Any lower base angle is supplementary to any upper base angle.
8. 8. Proving that a Quadrilateral is a ParallelogramIf both pairs of opposite sides of a quadrilateral is a parallelogram (definition)If both pairs of opposite sides of a quadrilateral are congruent, then it is aparallelogram.Fo two sides of a quadrilateral are both parallel and congruent, then it is aparallelogram.If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.If both pairs of opposite angles of a quadrilateral are congruent, then it is aparallelogram.
9. 9. Proving that a Quadrilateral is a RectangleIf a parallelogram contains at least one right angles, then it is arectangle (definition).If the diagonals of a parallelogram are congruent, then it is arectangle.If all four angles of a quadrilateral are right angles, then it is arectangle.
10. 10. Proving that a Quadrilateral is a Kite If two distinct pairs of adjacent sides of a quadrilateral are congruent, then it is a kite (definition). If one of the diagonals of a quadrilateral is the perpendicular bisector of the other diagonal, then it is a kite. If one of he diagonals is the angle bisector of the two opposite non-congruent angles.
11. 11. Proving that a Quadrilateral is a RhombusIf a parallelogram contains a pair of consecutive sides that arecongruent, then it is a rhombus (definition).If either diagonal of a parallelogram bisects two angles of theparallelogram, then it is a rhombus.If the diagonals of a quadrilateral are perpendicular bisectors ofeach other, then it is a rhombus.
12. 12. Proving that a Quadrilateral is a SquareIf a quadrilateral is both a rectangle and a rhombus, then it is asquare.
13. 13. Proving that a Trapezoid is an Isosceles Trapezoid If one nonparallel sides of a trapezoid are congruent, then it is isosceles (definition). If the lower or upper base angles of a trapezoid, then it is isosceles. If the diagonals of a trapezoid are congruent, then it is isosceles.
14. 14. The End!