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Geometry Unit 7
Properties of Quadrilaterals
Classifying Quadrilaterals:
Parallelogram
Rectangle
Square
Kite
Trapezoiod
Isosceles Trapezoid
Properties of Parallelograms
All properties on this page are true when a quadrilateral is a parallelogram
The opposite sides of a parallelogram are congruent.
Consecutive angles of a parallelogram are supplementary. (Consecutive interior angle theorem)
Opposite angles of a parallelogram are congruent.
Diagonals of a parallelogram bisect each other
Congruent segments theorem for parallel lines.
If three (or more) parallel lines make congruent segments on one transversal,
then they make congruent segments on all transversals.
Proving a quadrilateral is a parallelogram
Side Congruence: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a
parallelogram.
Opposite Angle Congruence: If both pairs of opposite angles of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Bisecting Diagonals: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a
parallelogram.
Congruent and Parallel: If one pair of opposite sides of a quadrilateral is both congruent and parallel, the
quadrilateral is a parallelogram.
Special Classes of Parallelograms
All Parallelogram rules apply as well as each shapes unique rules.
Rhombus: A parallelogram with all sides congruent.
The diagonals of a rhombus bisect their vertex angles.
The diagonals of a rhombus are Perpendicular.
Rectangle: A parallelogram with four right angles.
The diagonals of a Rectangle are congruent.
All vertex angles are congruent.
Square: A rectangle that is also a rhombus.
Ratio Rules for a Trapezoid
Trapezoid Midsegment Theorem: 1) The midsegment of a trapezoid is half the sum of the bases
2) The midsegment of a trapezoid is parallel to the bases of the
trapezoid.