Steps to Calculate Weighted Average
Geometry - Module 4 Help Sheet
Properties of Quadrilateral | |||||
Parallelogram | Rectangle | Square | Rhombus | Trapezoid | Kite |
| | | | | |
-Opposite sides are equal and parallel -Opposite angles are equal -Diagonals bisect each other -Consecutive angles are supp. | -Opposite sides are equal and parallel -All angles are equal (right angles) -Diagonals bisect each other | -Opposite sides are parallel -All four sides are equal -All angles are equal (right angles) -Diagonals bisect each other & are perpendicular | -Opposite sides are parallel -All four sides are equal -Opposite angles are equal -Diagonals bisect each other & are perpendicular | -One pair of opposite sides is parallel -The midsegment is parallel to the bases and half the sum of the bases | -Two pairs of adjacent sides are equal -One pair of opposite angles are equal -One diagonal bisects the other -Diagonals are perpendicular |
Distance Formula
D = √(x2 - x1)2 + (y2 - y1)2 , where (x1, y1) and (x2, y2) are coordinates
Slope Formula | ||
Slope is the steepness of a line. Found by | ||
Parallel Lines Lines that never intersect | Same slope | y = 2x + 7 y = 2x - 11 Both have a slope of 2, so they are parallel |
Perpendicular Lines Lines that intersect at a right angle | -Opposite sign AND reciprocal � slopes *The product of � perpendicular � slopes is � always -1 | y = ⅓x +5 y = -3x - 12 The slopes are ⅓ and -3, so the slopes are opposite reciprocals making the lines perpendicular |
( )
2 2
x1+x2 , y1+y2
Midpoint Formula
where (x1, y1) and (x2, y2) are coordinates
Perimeter: the distance around a figure (add all the side lengths)
Area: the space within a 2-dimensional figure
Area of a triangle: A = 1/2bh
Area of rectangle/square/parallelogram: A = bh
Area of a trapezoid: A = ½h(b1 + b2)
Slope-intercept form: y=mx+b
where m is the slope and b is the y-intercept
Point-slope form: y-y1 = m(x-x1)
where (x1, y1) is a point on the line
Standard form: Ax + By = C
where A is a positive whole number
Perimeter and Area
Equations of a Line
Classifying Triangles | |||
Right | Scalene | Isosceles | Equilateral |
One 90° ∠ | No ≅ sides | Two ≅ sides | Three ≅ sides |
Check for opposite & reciprocal slopes | Use the distance formula to find the side lengths | ||
The ratio 2:3 is read “two to three.” Finding the distance that is at a ratio of 2:3 between two points means the same as splitting the distance into 2 + 3 or 5 equal pieces and then finding 2 of those pieces.
M=