2 ParallelogramsDefinition: a quadrilateral having both pairs of opposite sides parallel to each other.
3 Properties The opposite sides are parallel The opposite sides are also congruentThe opposite angles are congruentThe diagonals bisect each otherBisects
4 Formulas for Parallelograms Perimeter = 2a + 2bArea = b x hThe 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
5 Properties we don’t Know The adjacents sides are parallel, so their measure is 180°x + y = 180°
6 RhombusDefinition: an equilateral parallelogram, including the square as a special case.
7 Properties of Rhombuses Have 4 equal/congruent/same sidesTheir diagonals are perpendicularDiagonals make right trianglesThe diagonals bisect their angles
8 Formulas Perimeter = all four sides added together x + x + x +x (x4) = perimeterArea = length of 2 diagonals times ½Area = ½ab
9 Properties of the Angles of a Rhombus (Stuff we don’t know yet) Adjacent sides of Rhombus are supplementary (Add up to 180°)
10 Rectangles Definition: a parallelogram having four right angles. gay rectangle
11 Properties of Rectangles Four right angles (all 90°)Diagonals are congruentThis picture is a rectangle!!!
12 Formulas of Rectangles Perimeter is the two lengths and the two heights added togetherl + l + w + w = perimeterArea is the length times the widthl x w = height
13 Special Quadrilaterals!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
14 TrapezoidsDefinition: a quadrilateral plane figure having two parallel and two nonparallel sides
15 Properties of Trapezoids Only have one set of parallel sidesThe midsegment is the average of the base lengthsThe midsegment is parallel to the basesThe angles on either side of the base are parallelThe diagonals are congruentThe adjacent angles are parallel (Add up to 180°)b = base, a = leg
16 Formulas of Trapezoids Perimeter is the length of every sideleg1 + leg2 + base1 + base2 = perimeterArea is the ½ of the height times both of the bases added togetherArea = ½ h (b + b)
17 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!!!!!!!!
18 KitesThere’s no definition, but it looks like a kite!Gay kite!
19 Properties of a Kite Two pairs of congruent sides Two of the sides aren’t congruentThe diagonals are perpendicularOne pair of the opposite angles are congruentThe intersection of the diagonals make right triangles (Because they’re perpendicular)The long diagonal bisects the short one
20 Formulas for Kites The perimeter is all of the sides added a + a + b + b = perimeterAdd the two diagonals and divide by 2 or multiply by ½area = ½ ab
21 (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!)
22 Properties of Isosceles Trapezoids Pairs of the base angles are congruentDiagonals are congruentThe angles on either side of the bases are the same size