Unit 5 - Quadrilaterals and Polygons

Parallelogram

• Opposite sides are parallel

• Opposite sides are congruent

• Opposite angles are congruent

• Consecutive angles are supplementary (angles that are next to each other)

• Diagonals bisect eachother

Rectangle

• All angles are right angles

• Diagonals are congruent

Rhombus

• All sides are congruent

• Diagonals bisect the angles

• Diagonals form perpendicular bisectors

• Diagonals divide rhombus into four congruent right angles

Square

• ALL OF THE PROPERTIES FROM PARALLELOGRAM, RECTANGLE, AND RHOMBUS

Trapezoid/Isosceles trapezoid

• Trapezoid

  • Bases are parallel

• Isosceles trapezoid

  • Legs are congruent

  • Diagonals are congruent

  • Lower base angles are congruent

  • Upper base angles are congruent

  • Any lower base is supplementary to any upper base

If we find our distance between points is equal…

Segments are congruent

If we find our slopes are the same…

There are parallel segments

If we find our slopes are opposite reciprocals…

There are perpen6dicular segments

If we find our midpoints are the same

Segments bisect

Parallelogram area formula

A = b x h

Rectangle area formula

A = b x h

Rhombus area formula

A = ½ (d 1) (d 2)

Trapezoid area formula

A = ½ (b 1 + b 2) h

Sum of the interior angles of a n sided polygon

(n - 2) x 180

n = number of sides

180 = sum of angles in a triangle

Sum of the exterior angles of an n sided polygon

360 degrees

Regular polygons

• Equilateral - All sides are congruent to each other

• Equiangular - All angles are congruent to each other

Regular polygon area formula (with n sides)

A = ½ (base side) (height of one triangle) (n)

n = number of sides

Equation makes area of one triangle, but double that if you are calculating half