Geometry Flashcards
What are supplementary angles?
Sum of angles equal 180deg
What are complementary angles?
Sum of angles equal 90deg
A cyclic quadrilateral (quad with vertices on circle circumference) have what property?
Opposite angles are supplementary (sum equals 180deg)
For a regular polygon, what are the equations to find the:
1. Interior Angles
2. Exterior Angles
- IA = (n-2)/2 x 180deg
- EA = 360/n
For any polygon, what are the equations to find the sum of the:
1. Interior Angles
2. Exterior Angles
- Sum(IA) = (n-2) x 180deg
- Sum(EA) = 360
What are the two equation forms of a linear line in coordinate geometry?
- Standard: ax + by +c = 0
- Slope/Intercept: y = mx +c
In coordinate geometry, when a linear equation has 1 variable, it has what relationship to the axes?
It is parallel to one of the axes
How do you calculate the midpoint between 2 coordinates?
MP = ( (X1+ X1)/2, (Y1 + Y1)/2)
How do you find the gradient between 2 points?
(y2 - y1) / (x2 - x1)
How do you calculate the distance of coordinates from the origin?
Distance = sqrt((x^2) + (y^2))
In coordinate geometry, how do you calculate the distance between two points?
sqrt( (x1-x2)^2 + (y1-y2)^2 )
If a triangle on a coordinate plane has no sides parallel to the axis, how do you find the area?
Area under the graph - Area not included
In a coordinate plane how do you know if 2 lines are perpendicular?
Product of gradients =1
IOW gradients are reciprocal
OR
(a1a2) = (b1b2)
What is the area of a trapezium?
A = (1/2)(a+b)h
In a coordinate plane how do you know if 2 lines intersect?
(a1/a2) =/= (b1/b2)
In a coordinate plane how do you know if 2 lines are coincident?
(a1/a2) = (b1/b2) = (c1/c2)
In a coordinate plane how do you know if 2 lines are parallel?
(a1/a2) = (b1/b2) =/= (c1/c2)
For a cuboid how do you find:
1. Body Diagonal
2. Face Diagonal
3. Minimum surface distance?
- db = sqrt(l^2 + w^2 + h^2)
- df = sqrt(l^2 + w^2)
- Min SD = sqrt(l^2 + (w + h)^2)
When two tangents on a circle meet at a point, what is the relationship between the tangents?
They are equal length
How do you find the diameter for:
1. A cylinder in a cube
2. A cube in a cylinder
- d = side
- d = df = sqrt(2) . side
How do you find the area of a segment?
(pi) . r^2 . (angle/360) - area of triangle
Angle/360 is equal to the number of sectors if the sectors are equal
How do you find the length of:
1. Minor arc
2. Major arc
- Minor arc = (2x pi x r x angle)/360
- Major arc = (2x pi x r x (360-angle))/360
All angles in a segment =?
90deg
How do you find the area of a sector?
(pi) . r^2 . (angle/360)
Angle/360 is equal to the number of sectors if the sectors are equal
How do you find the diameter for:
1. A sphere in a cube
2. A cube in a sphere
- d = cube side length
- d = cube body diagonal = s x sqrt(3)
If an equilateral triangle is inscribed in a circle, r = ?
r = side/(sqrt(3))
If a circle is inscribed in an equilateral triangle, r = ?
r = side/(2.(sqrt(3)))
For a cube how do you find:
1. Body Diagonal
2. Face Diagonal
3. Minimum surface distance?
- db = sqrt(3) . side
- df = sqrt(2) . side
- Min SD = sqrt(5) . side
For a hemisphere how do you find:
1. Curved Surface Area
2. Total Surface Area
3. Volume?
- Curved SA = 2(pi)(r^2)
- Total SA = 3(pi)(r^2)
- Volume = (2/3)(pi)(r^3)
For a sphere how do you find:
1. Total Surface Area
2. Volume?
- SA = 4(pi)(r^2)
- Volume = (4/3)(pi)(r^3)
What is the area of a trapezium?
A = (1/2)(a+b)h
For a regular polygon, the perimeter is what when the area is what?
Perimeter is maximum when area is minimum
Perimeter is minimum when area is maximum
How do you find the central angle of a regular polygon?
360deg/n
n is the number of sides
What is the equation for the diagonal of a square?
sqrt(2).s
The diagonals of a rhombus have what relationship?
They are perpendicular
What is the equation for the diagonal of a rectangle?
Diagonal = sqrt((b^2) + (h^2))
What are the 3 methods to find if two triangles are congruent?
- SAS
- SSS
- SAA
The diagonals of a rectangle have what relationship?
The bisect eachother and so, have equal length
What is the relationship between z^2 and (x^2 + y^2) for:
1. * An acute triangle
1. * An obtuse triangle ?
- z^2 < x^2 + y^2
- z^2 > x^2 + y^2
Congruent triangles have what relationship?
- All respective sides are the same
- All respective angles are the same
Similar triangles have what relationship?
- All respective sides are proportional
- All respective angles are the same
When diagonals bisect you make 2 (what) triangles?
congruent
What are the 3 methods to find if two triangles are similar?
- SAS
- SSS
- AA
For a triangle with sides A, B, C what is the relationship with C if:
1. * A + B
2. * A - B?
- A + B > C
- A - B < C
How do you solve: What is the difference between the area/volume of a shape and the shape with a maximum error (x)
Add the error to the original dimensions to find the individual difference for l, w, h and sum the differences
sum(diff) = l(diff) + w(diff) + h(diff)
