Quadrilaterals and Other Polygons

Polygon

A closed plane figure formed by three or more line segments

Convex

Having no indentations

Concave

Having one or more indentations

Regular polygons

Polygons that are convex, equilateral, & equiangular

Diagonals

Line segments that connect two non consecutive vertices of a polygon (divides polygons into triangles)

Formula to find sum of angle measurements in polygon

(n-2)180

formula to find measure of exterior angle

360/n = measure of each exterior angle

Quadrilateral

A polygon with 4 sides

parallelogram

a quadrilateral with both pairs of opposite sides are parallel, opposite sides & angles are congruent.

consecutive angles of a parallelogram

are supplementary

The diagonals of a parallelogram

bisect each other

The quadrilateral is a parallellogram if even

-If opposite sides in a quadrilateral are congruent

-if just one pair of opposite sides are both parallel & congruent

-if opposite angles are congruent

-if all pairs of consecutive angles are supplementary

-if diagonals bisect each other

rectangles

A quadrilateral with four right anfles

A parallelogram is a rectangle if,

• the diagonals are congruent

• if ONE angle measures 90 degrees

Rhombus

A quadrilateral with four congruent sides

a parallelogram is a rhombus if,

• the diagonals are perpendicular

• had two adjacent sides that are congruent

Square

A quadrilateral with four right angles & four congruent sides (ALL OF THE QUALITIES OF A RHOMBUS AND RECTANGLE)

Trapezoid

a quadrilateral with exactly one pair of parallel sides

median of a trapezoid

a line that connects the midpoint of a trapezoid’s legs, parallel to both sides and the average of base lengths

isosceles trapezoid

A trapezoid with two congruent legs, base angles are congruent, adjacent non-congruent angles are supplementary, diagonals are congruent