Quadrilaterals

Bryce Hall4 Wennersten

ParallelogramsDefinition: a quadrilateral having both pairs of opposite sides parallel to each other.

Properties• The opposite sides are parallel• The opposite sides are also

congruent• The opposite angles are congruent• The diagonals bisect each other

Bisects

Formulas for Parallelograms• Perimeter = 2a + 2b• Area = b x h– The area is b x h because a

parallelogram is basically just two right triangles and a rectangle, so the area = length x width and length x width = b x h :3

Properties we don’t Know

• The adjacents sides are parallel, so their measure is 180°

x + y = 180°

Rhombus• Definition: an equilateral

parallelogram, including the square as a special case.

Properties of Rhombuses• Have 4 equal/congruent/same sides• Their diagonals are perpendicular– Diagonals make right triangles

• The diagonals bisect their angles

Formulas• Perimeter = all four sides added

together– x + x + x +x (x4) = perimeter

• Area = length of 2 diagonals times ½– Area = ½ab

Properties of the Angles of a Rhombus(Stuff we don’t know yet)

• Adjacent sides of Rhombus are supplementary (Add up to 180°)

RectanglesDefinition: a parallelogram having four right angles.

gay rectangle

Properties of Rectangles• Four right angles (all 90°)• Diagonals are congruent

This picture is a rectangle!!!

Formulas of Rectangles• Perimeter is the two lengths and the

two heights added together– l + l + w + w = perimeter

• Area is the length times the width– l x w = height

Special Quadrilaterals!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!

Trapezoids• Definition: a quadrilateral plane figure

having two parallel and two nonparallel sides

Properties of Trapezoids• Only have one set of parallel sides• The midsegment is the average of the base

lengths• The midsegment is parallel to the bases• The angles on either side of the base are parallel• The diagonals are congruent• The adjacent angles are parallel (Add up to 180°)

b = base, a = leg

Formulas of Trapezoids• Perimeter is the length of every side– leg1 + leg2 + base1 + base2 =

perimeter• Area is the ½ of the height times

both of the bases added together– Area = ½ h (b + b)

Why we use the formula ½ h (b + b) for area of a Trapezoid

• The formula is based on two identical trapezoids side by side, so they’re a parallelogram!!!!

• We have to use the formula for parallelograms ( base x height)

• Since the are of this figurative parallelogram is two of the trapezoids, we find ½ of it!!!!!!!!

Kites• There’s no definition, but it looks like a

kite!

Gay kite!

Properties of a Kite• Two pairs of congruent sides• Two of the sides aren’t congruent• The diagonals are perpendicular• One pair of the opposite angles are congruent• The intersection of the diagonals make right

triangles (Because they’re perpendicular)• The long diagonal bisects the short one

Formulas for Kites• The perimeter is all of the sides added– a + a + b + b = perimeter

• Add the two diagonals and divide by 2 or multiply by ½– area = ½ ab

Isosceles trapezoids• There’s no definition, but an

isosceles trapezoid has one pair of equal sides!!!!!!!

(Isosceles trapezoids have the same formulas as normal trapezoids!)

Properties of Isosceles Trapezoids

• Pairs of the base angles are congruent

• Diagonals are congruent• The angles on either side of the

bases are the same size