Geometry Flashcards
Triangles Perimeter
P = A + B + C
Triangle Area
A = (B×H) ÷ 2
Specific triangles
30-60-30 = 1:sqrt(3):2 - 45-45-90 = 1:1:sqrt(2)
Square properties
All opposites sides are parallel and have the same length. All angles are 90°. Diagonal have the same length, intersect at 90° and bisect each other. Interior angles add up to 360°.
Square area
A = s2
Square perimeter
P = 4s
Square key shapes
Diagonals create two 45-45-90 isoceles right triangles.
Rectangle properties
All opposites sides are parallel. Opposite sides are the same length. All angles are 90°. Diagonals are the same length and bisect each other. Interior angles add up to 360°.
Rectangle area
A = l × w
Rectangle perimeter
P = 2l + 2w
Rectangle key shapes
Diagonals create 2 right triangles.
Parallelogram properties
All opposites sides are parallel. Opposite sides are the same length. Opposite angles are equal. Diagonals bisect each other. Interior angles add up to 360°.
Parallelogram area
A = b × h
Parallelogram perimeter
P = 2a + 2b
Parallelogram key shapes
Right triangle needed to find the height.
Trapezoid properties
2 sides are parallel. Interior angles add up to 360°.
Trapezoid area
A = 1/2 (b+c)h with b and c the length of the parallel sides.
Trapezoid perimeter
P = a + b + c + d
Trapezoid key shapes
Right triangle needed to find the height.
Sum of angles of a polygon
SoA = (n-2)×180 (with n the number of sides)
Circle area
A = πr^2
Circle circumference
C = 2πr
Circle arc length
AL = 2πr ( x/360 ) with x the central angle measure
Circle - Similar inscribed angles
All inscribed angles that extend to the same arc or same two points on a circle are equal.
Circle - Central angle x vs. inscribed angle y
Any central angle that extends to the same arc or same two points on a circle as does an inscribed angle is twice the size of the inscribed angle. x = 2y
Circle - Triangles inscribed in a semicircle
Any triangle inscribed in a semicircle with the circle diameter as longer side is always a right triangle.
3D figures - Volume
V = (area of 2-D surface)×h
Cube volume
V = s3
Cube surface area
SA = 6s2
Cube longest length within
L = sqrt(3s^2)
Rectangular solid volume
V = lwh
Rectangular solid surface area
SA = 2lw + 2lh + 2hw
Rectangular solid longest length within
L = sqrt( l^2 + w^2 + h^2 )
Cylinder volume
V = π×r^2×h
Cylinder surface area
SA = 2(πr^2) + 2πrh
Cylinder longest length within
L = sqrt(4r^2 + h^2)
Cylinder longest length within
L = sqrt(4r^2 + h^2)
Cylinder longest length within
L = sqrt(4r^2 + h^2)
Sphere volume
V = (4/3)πr^3
Sphere surface area
SA = 4πr^2
Sphere longest length within
L = 2r
Slope intercept formula
y = mx + b with m the slope, b the y-intercept and (-b/m) the x-intercept.
Slope of a line
Δy / Δx = (y2 - y1) / (x2 - x1)
x- and y-intercepts
1 - Use y = mx + b formula. 2 - Set x equal to 0 to find the y-intercept. Set y equal to 0 to find the x-intercept.
Calculating intersections of two lines
Set both equations equal to each other and resolve. (l1) : y=ax+b ; (l2) : y=mx+p –> ax+b=mx+p
Distance between any two points
(p1) : (x1, y1) ; (p2) : (x2, y2) –> d(p1, p2) = sqrt( (Δx)^2 + (Δy)^2 ) = sqrt( (x1-x2)^2 + (y1-y2)^2 )
Midpoint formula
(p1) : (x1, y1) ; (p2) : (x2, y2) –> Midpoint = ( (x1+x2)/2, (y1+y2)/2 )
