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Quadrilaterals Bryce Hall 4 Wennersten
Parallelograms Definition: 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°)
Rectangles Definition: a parallelogram having four right angles.
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
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 have the same formulas as normal 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
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