Advanced Geometry 5.4 / 5 Four Sided Polygons /  
 Properties of Quadrilaterals Learner Objective: I will solve problems using properties 
 of special quadrilaterals.

Polygon  Plane Figure  Consists only of segments  Consecutive sides intersect only at endpoints  Non-Consecutive sides do not intersect  Each vertex belongs to exactly two sides  Convex Polygon  A polygon in which each interior angle has a measure less than 180.  Concave Polygon  A polygon in which at least one interior angle has a measure greater 
 than 180.  Diagonal of a Polygon  Any segment that connects two nonconsecutive (nonadjacent) 
 vertices of the polygon is a Diagonal of the Polygon.

Quadrilateral: A four sided Polygon Special Quadrilaterals Parallelogram:  Definition: A Parallelogram is a Quadrilateral in which both pairs of 
 opposite sides are parallel. Properties:  Opposite sides are congruent  Opposite angles are congruent  Diagonals bisect each other Any pair of consecutive angles are supplementary

Rectangle:  Definition: A Rectangle is a Parallelogram in which at least one angle is a 
 right angle.  Properties:  All properties of a Parallelogram apply by definition  All angles are right angles  The diagonals are congruent

Rhombus:  Definition: A Rhombus is a Parallelogram in which at least two consecutive 
 sides are congruent.  Properties:  All properties of a Parallelogram apply by definition  All sides are congruent  Diagonals are perpendicular bisectors of each other  Diagonals bisect the angles  Diagonals divide the rhombus into four congruent right triangles

Square:  Definition: A Square is a Parallelogram that is both a Rectangle and a 
 Rhombus.  Properties:  All properties of a rectangle apply by definition  All properties of a rhombus apply by definition  The diagonals form four isosceles right triangles (45⁰-45⁰-90⁰)

Kite:  Definition: A Kite is a quadrilateral in which two disjoint pairs of consecutive 
 sides are congruent.  Properties:  Diagonals are perpendicular  One diagonal is the perpendicular bisector of the other  One diagonal bisects a pair of opposite angles  One pair of opposite angles are congruent

Trapezoid:  Definition: A Trapezoid is a quadrilateral with exactly one pair of parallel 
 sides. The parallel sides are called bases of the trapezoid.

Isosceles Trapezoid:  Definition: An Isosceles Trapezoid is a trapezoid in which the nonparallel 
 sides (legs) are congruent.  Properties:  Legs congruent by definition  Bases parallel by definition  Lower base angles congruent  Upper base angles congruent  Diagonals are congruent  Any lower base angle is supplementary to any upper base angle

_______ rhombuses are squares _______ squares are rhombuses quadrilateral parallelogram trapezoid isosceles trapezoid rectangle square rhombus kite kite kite Some All No _______ rhombuses are squares _______ squares are rhombuses _______ rhombuses are kites _______ trapezoids are rectangles _______ rectangles are parallelograms _______ kites are rhombuses _______ trapezoids are parallelograms _______ rectangles are rhombuses _______ squares are rectangles _______ parallelograms are quadrilaterals _______ isosceles trapezoids are parallelograms

STATEMENTS REASONS