Geometry Flashcards by Jessica Summersby

What are supplementary angles?

Sum of angles equal 180deg

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What are complementary angles?

Sum of angles equal 90deg

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A cyclic quadrilateral (quad with vertices on circle circumference) have what property?

Opposite angles are supplementary (sum equals 180deg)

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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

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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

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What are the two equation forms of a linear line in coordinate geometry?

Standard: ax + by +c = 0
Slope/Intercept: y = mx +c

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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

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How do you calculate the midpoint between 2 coordinates?

MP = ( (X1+ X1)/2, (Y1 + Y1)/2)

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How do you find the gradient between 2 points?

(y2 - y1) / (x2 - x1)

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How do you calculate the distance of coordinates from the origin?

Distance = sqrt((x^2) + (y^2))

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In coordinate geometry, how do you calculate the distance between two points?

sqrt( (x1-x2)^2 + (y1-y2)^2 )

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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

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In a coordinate plane how do you know if 2 lines are perpendicular?

Product of gradients =1
IOW gradients are reciprocal
OR
(a1a2) = (b1b2)

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What is the area of a trapezium?

A = (1/2)(a+b)h

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In a coordinate plane how do you know if 2 lines intersect?

(a1/a2) =/= (b1/b2)

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In a coordinate plane how do you know if 2 lines are coincident?

(a1/a2) = (b1/b2) = (c1/c2)

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In a coordinate plane how do you know if 2 lines are parallel?

(a1/a2) = (b1/b2) =/= (c1/c2)

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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)

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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

1. d = cube side length 2. 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?

1. db = sqrt(3) . side 2. df = sqrt(2) . side 3. Min SD = sqrt(5) . side

For a hemisphere how do you find: 1. Curved Surface Area 2. Total Surface Area 3. Volume?

1. Curved SA = 2(pi)(r^2) 2. Total SA = 3(pi)(r^2) 3. Volume = (2/3)(pi)(r^3)

For a sphere how do you find: 1. Total Surface Area 2. Volume?

1. SA = 4(pi)(r^2) 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?

1. SAS 2. SSS 3. 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 ?

1. z^2 < x^2 + y^2 2. z^2 > x^2 + y^2

Congruent triangles have what relationship?

1. All respective sides are the same 2. All respective angles are the same

Similar triangles have what relationship?

1. All respective sides are proportional 2. 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?

1. SAS 2. SSS 3. AA

For a triangle with sides A, B, C what is the relationship with C if: 1. * A + B 2. * A - B?

1. A + B > C 2. 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)