Geometry

Question 1

What are supplementary angles?

Answer 1

Sum of angles equal 180deg

Question 2

What are complementary angles?

Answer 2

Sum of angles equal 90deg

Question 3

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

Answer 3

Opposite angles are supplementary (sum equals 180deg)

Question 4

For a regular polygon, what are the equations to find the:
1. Interior Angles
2. Exterior Angles

Answer 4

1. IA = (n-2)/2 x 180deg
2. EA = 360/n

Question 5

For any polygon, what are the equations to find the sum of the:
1. Interior Angles
2. Exterior Angles

Answer 5

1. Sum(IA) = (n-2) x 180deg
2. Sum(EA) = 360

Question 6

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

Answer 6

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

Question 7

In coordinate geometry, when a linear equation has 1 variable, it has what relationship to the axes?

Answer 7

It is parallel to one of the axes

Question 8

How do you calculate the midpoint between 2 coordinates?

Answer 8

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

Question 9

How do you find the gradient between 2 points?

Answer 9

(y2 - y1) / (x2 - x1)

Question 10

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

Answer 10

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

Question 11

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

Answer 11

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

Question 12

If a triangle on a coordinate plane has no sides parallel to the axis, how do you find the area?

Answer 12

Area under the graph - Area not included

Question 13

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

Answer 13

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

Question 14

What is the area of a trapezium?

Answer 14

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

Question 15

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

Answer 15

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

Question 16

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

Answer 16

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

Question 17

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

Answer 17

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

Question 18

For a cuboid how do you find:
1. Body Diagonal
2. Face Diagonal
3. Minimum surface distance?

Answer 18

1. db = sqrt(l^2 + w^2 + h^2)
2. df = sqrt(l^2 + w^2)
3. Min SD = sqrt(l^2 + (w + h)^2)

Question 19

When two tangents on a circle meet at a point, what is the relationship between the tangents?

Answer 19

They are equal length

Question 20

How do you find the diameter for:
1. A cylinder in a cube
2. A cube in a cylinder

Answer 20

1. d = side
2. d = df = sqrt(2) . side

Question 21

How do you find the area of a segment?

Answer 21

(pi) . r^2 . (angle/360) - area of triangle

Angle/360 is equal to the number of sectors if the sectors are equal

Question 22

How do you find the length of:
1. Minor arc
2. Major arc

Answer 22

1. Minor arc = (2x pi x r x angle)/360
2. Major arc = (2x pi x r x (360-angle))/360

Question 23

All angles in a segment =?

Answer 23

90deg

Question 24

How do you find the area of a sector?

Answer 24

(pi) . r^2 . (angle/360)

Angle/360 is equal to the number of sectors if the sectors are equal

Question 25

How do you find the diameter for:
1. A sphere in a cube
2. A cube in a sphere

Answer 25

1. d = cube side length
2. d = cube body diagonal = s x sqrt(3)

Question 26

If an equilateral triangle is inscribed in a circle, r = ?

Answer 26

r = side/(sqrt(3))

Question 27

If a circle is inscribed in an equilateral triangle, r = ?

Answer 27

r = side/(2.(sqrt(3)))

Question 28

For a cube how do you find:
1. Body Diagonal
2. Face Diagonal
3. Minimum surface distance?

Answer 28

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

Question 29

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

Answer 29

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

Question 30

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

Answer 30

1. SA = 4(pi)(r^2)
2. Volume = (4/3)(pi)(r^3)

Question 31

What is the area of a trapezium?

Answer 31

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

Question 32

For a regular polygon, the perimeter is what when the area is what?

Answer 32

Perimeter is maximum when area is minimum
Perimeter is minimum when area is maximum

Question 33

How do you find the central angle of a regular polygon?

Answer 33

360deg/n

n is the number of sides

Question 34

What is the equation for the diagonal of a square?

Answer 34

sqrt(2).s

Question 35

The diagonals of a rhombus have what relationship?

Answer 35

They are perpendicular

Question 36

What is the equation for the diagonal of a rectangle?

Answer 36

Diagonal = sqrt((b^2) + (h^2))

Question 37

What are the 3 methods to find if two triangles are congruent?

Answer 37

1. SAS
2. SSS
3. SAA

Question 38

The diagonals of a rectangle have what relationship?

Answer 38

The bisect eachother and so, have equal length

Question 39

What is the relationship between z^2 and (x^2 + y^2) for:
1. * An acute triangle
1. * An obtuse triangle ?

Answer 39

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

Question 40

Congruent triangles have what relationship?

Answer 40

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

Question 41

Similar triangles have what relationship?

Answer 41

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

Question 42

When diagonals bisect you make 2 (what) triangles?

Answer 42

congruent

Question 43

What are the 3 methods to find if two triangles are similar?

Answer 43

1. SAS
2. SSS
3. AA

Question 44

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

Answer 44

1. A + B > C
2. A - B < C

Question 45

How do you solve: What is the difference between the area/volume of a shape and the shape with a maximum error (x)

Answer 45

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)