Quadrilaterals and Polygons SOL Review Session

Names of Polygons Number of SidesName

Regular Polygon  All sides and all angles are congruent

Formulas  Sum of the interior angles  Sum of the exterior angles  One interior angle of regular polygon  One exterior angle of a regular polygon

x x x Find the sum of the exterior angles of a hexagon. Examples with Polygons

Venn Diagram of Quadrilaterals

Flow Chart of Quadrilaterals

Parallelogram  Opposite sides are congruent  Opposite angles are congruent  Consecutive angles are supplementary  Diagonals bisect each other

Examples with Parallelograms 110 ab c 5 8 x y 8 a7 b x

Rectangles  Opposite sides are congruent  All angles are equal Opposite angles are equal Consecutive angles are supplementary  Diagonals bisect each other  Diagonals are congruent

Examples with Rectangles 7 4 a b A B CD If AC = 3x – 10 and BD = x + 24, find AC. c

Rhombus  All sides are equal Opposite sides are equal  Opposite angles are congruent  Consecutive angles are supplementary  Diagonals bisect each other  Diagonals bisect the angles  Diagonals are perpendicular

Examples with Rhombi 5x Solve for x. 22 a b c d

Square  All sides are equal Opposite angles are congruent  All angles are congruent Opposite angles are congruent Consecutive angles are supplementary  Diagonals bisect each other  Diagonals bisect the angles  Diagonals are congruent  Diagonals are perpendicular

Examples with Squares A B CD E If AB = 6x + 3 and BC = 4x + 11, find AB. If m<AEB = 10x, find x.

Trapezoid One pair of opposite sides are parallel  Isosceles Trapezoid One pair of opposite sides are parallel The two legs are congruent Base angles are congruent Diagonals are congruent Base leg

Median of a Trapezoid AB CD EF If AB = 28 and CD = 12, find EF. If AB = 32 and EF = 14, find CD.