Geometry Flashcards
Triangle (Formulas)
perimeter = sum of the lengths of the 3 sides
area = base*height/2
height of a right triangle is shortest side, if not a right triangle you must draw in height
pythagorean theorem: a^2 + b^2 = c^2
Pythagorean Triples
3: 4: 5
5: 12: 13
7: 24: 25
8: 15: 17
9: 40: 41
Right Triangle 30-60-90 proportions
x: x√3: 2x
Right Isosceles Triangle 45-45-90 proportions
x: x: x√2
Axis
y axis is vertical
x axis is horizontal
Standard form of a line
y = mx + b m = slope b = y-int
Slope
Δ y / Δ x
rise/run = y2 -y1 / x2 - x1
parallel lines have same slope
perpendicular lines have negative reciprocal slope
Lines and Angles
- vertical angles are equal
- the sum of angles that form a straight line = 180
- when two parallel lines are intersected by a third line (transversal), the corresponding angles are equal
Polygons
- formed by 3 or more line segments
- (n-2)180 = the sum of the interior angle measures of a polygon with n sides
- perimeter = sum of sides
Triangles
- interior angles sum to 180
- every external angle of a triangle equals the sum of the 2 noncorresponding internal angles
- in any triangle, a side opposite a greater angle is longer than a side opposite a smaller angle, and sides opposite equal angles are equal
- every side of triangle must be longer than the difference of the lengths of the other 2 sides
- equilateral: sides are equal, angles equal
- isosceles: 2 sides of equal length (opposite angles of the equal sides are equal)
- right: one angle equals 90, longest side of triangle is opposite 90 angle (hypotenuse)
- pythagorean triples for right triangles only
Parallelogram (includes rectangles and squares)
height won’t be the side of the figure (may have to draw in)
- opposite sides equal so opposite angles equal
- area = bh
- perimeter = sum of all sides
Trapezoid
area = 1/2 (b1 + b2)h
Circle
- area = TTr^2
- circumference = TTd
- arc length = 1/n(circumference), where n is the fraction of the portion of circle n/360
- area of sector = 1/n(area)
- triangle is inscribed in semicircle when one its sides is diameter of circle, with other 2 sides meeting at any point on circle (inscribed triangles always right triangles)
Multiple figures
- break the figures down to simpler figures
- look for SHARED measurements
Solids
volume = l x w x d (rectangle, cube)
volume = area of base x depth
- cylinder = TTr^2 (depth)
surface area = sum of ALL areas from ALL faces
Coordinate geometry
- every point has ordered pair (x,y)
- able to find m if you know any 2 point on the line
- one way to find distance in coordinate plan is with pythagorean theorem (note special right triangles)
Rule of triangles
Every side must be larger than the difference between the other two sides and shorter than their sum
