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Maths > Section 5 - Geometry And Measures > Flashcards

Section 5 - Geometry And Measures Flashcards

1
Q

Tell me the 5 simple rules of geometry

A

Angles in triangle add to 180 degrees

Angles on a straight line add up to 180

Angles in a quadrilateral add to 360

Angles on a round point add to 360

Isosceles triangle have 2 sides the same and 2 angles the same

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2
Q

Tell me about angles around parallel lines

A

The 2 bunches of angles formed at the points of intersection are the same

There are only 2 different angles involved and add to 180 on a parallel line

Vertically opposite angles are equal

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3
Q

Tell me about alternate angles

A

Alternate angles are the same and found in a Z shape

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4
Q

Tell me about allied/ interior angles

A

Allied angles add to 180 and found in a c or u shape

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5
Q

Tell me about corresponding angles

A

They are the same, found in an f shape

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6
Q

What’s 3 letter notation

A

Eg angle abc is referring angle formed at b - might see it as b with a little hat

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7
Q

What’s a polygon

A

Can be regular or irregular

A regular polygon is where all the sides and angles are the same

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8
Q

List some regular polygon names

A 
Equilateral triangle 
Square
Pentagon
Hexagon
Heptagon
Octagon
Nonagon 
Decagon
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9
Q

What are the sum of exterior angles in a polygon

For any polygon

A

360 degrees

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10
Q

How do you work out the sum of interior angles in a polygon

For any polygon

A

(N - 2) X 180

N= number of sides

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11
Q

How do you work out an exterior angle of a regular polygon

A

360 divided by n (number of sides)

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12
Q

How do you work out the interior angles in a regular polygon

A

180 - exterior angle

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13
Q

Tell me about equilateral triangles

A

3 equal sides
3 equal angles of 60 degrees

3 lines of symmetry

Rotation symmetry order 3 (how many turns on each side to do 360 degrees)

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14
Q

Tell me about right angled triangles

A

1 right angle

No lines of symmetry

No rotational symmetry

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15
Q

Tell me about isosceles triangles

A

2 sides are the same

2 angles the same

1 line of symmetry

No rotational symmetry

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16
Q

Tell me about scalene triangles

A

All 3 different sides

All three different angles

No symmetry

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17
Q

Tell me about squares

A

4 equal angles

4 lines lf symmetry

Rotational symmetry order 4

Diagonals are the same length and cross at right angles

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18
Q

Tell me about rectangles

A

4 equal angles

2 lines of symmetry

Rotational symmetry order of 2

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19
Q

Tell me about rhombus

A

Same as diamond, a square pushed over

4 equal sides

2 pairs of equal angles - opposite angles equal
Neighbouring angles add to 180

2 lines of symmetry and a rotational symmetry order 2

Diagonals cross at right angles

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20
Q

Tell me about parallelogram

A

A rectangle pushed over

2 pairs of equal sides
2 pairs of equal angles
- opposites equal and interior add to 180

No lines of symmetry

Rotational symmetry order of 2

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21
Q

Tell me about trapezium

A

1 pair of parallel sides

No lines of symmetry
No rotational symmetry

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22
Q

Tell me about kites

A

2 pairs of equal sides
1 pair of equal angles

1 line of symmetry

No rotational symmetry

Diagonals cross at right angles

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23
Q

Tell me the rules of a circle

A

A tangent and a radius meet at 90 degrees

2 radi form an isosceles triangle

The perpendicular dissector of a chord passes through the centre of the circle

The angle at the centre of the circle is twice the angle at the circumference

The angle in a semicircle is 90 degrees

Angles in the same segment are equal

The opposite angles in a cyclic quadrilateral add to 180

Tangents from the same point are the same length

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24
Q

Tell me about the alternate segment theorem

A

The angle between a tangent and a chord is always equal to the angle in the opposite segment

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25
What's congruence
If two shapes are congruent, they are the same size and shape They could be reflected or rotated
26
How do you prove two triangles are congruent
Show one of the 4 conditions (next questions)
27
What's SSS
Where three sides are the same
28
What's AAS
Two angles and a corresponding side match up
29
Tell me about SAS
Two sides and the angle between them match up
30
Tell me about RHS
A right angle, the hypotenuse and one other side all match up
31
What are similar shapes
They are the same shape but are different sizes
32
Tell me how triangles can be similar
Triangles are similar if All the angles match up All 3 sides are proportional Any two sides are proportional and the angle between them is the same
33
Tell me about the translation transformation
The amount the shale moves is given by a vector written (X/y) X is horizontal movement Y is vertical movement Left and down is negative Shapes are congruent When answering say translation by the vector (X/y)
34
Tell me about the rotation transformation
You must give 3 details The angle of rotation The direction of rotation - clockwise or anti-clockwise The centre of rotation - often the origin Shapes are congruent under rotation Answer like A transformation from shape a to b is a rotation of 90 degrees anti-clockwise ABOUT the origin
35
Tell me about reflections
You must give the equation of the mirror line Shapes are congruent under reflection Eg a reflection in the line y = X Points are invariant if they remain the same after a transformation - for reflection any point on mirror line will be invariant
36
Tell me about enlargements
You must specify The scale factor The centre of enlargement The scale factor is the new length divided by the old length Eg an enlargement of scale factor 2, centre (0,3) (for example)
37
Tell me the key facts of scale factors
If the scale factor is bigger than 1, shape gets bigger Scale factor is smaller than 1 - eg 1/2 shape gets smaller If the scale factor is negative - shape pops out other side of enlargement centre. Eg -1 would be same size and shape with a rotation of 180 The scale factor tells you the relative distance of old points and new points from the centre of enlargement
38
How do you work out the area of a triangle
1/2 X b X h (vertical height)
39
How do you calculate the area of a parallelogram
B X h (vertical height)
40
How do you calculate the area of trapezium
1/2(a + b) X h (vertical height) A = opposite side of base
41
How do you calculate the area of circle
Pi X r^2
42
How do you calculate circumference
Pi X diameter
43
How do you work out the area of a sector (area of a circle)
X divided by 360 x area of full circle X = angle
44
How do ylu work out the length of an arc
X/360 X circumference of full circle
45
What does exact area mean
Leave answer in terms of pi for circles eg 3 pi
46
What's are vertices / a vertex
Corners
47
What's surface area
Only applied to 3D objects - it's just the total area of all the faces added together Surface area of solid = area of net
48
What's the surface area of a sphere
4 X pi X radius squared
49
How do you work out the surface area of a cone
Pi X radius X slant height + pi X radius squared
50
How do you work out the surface area of a cylinder
2 X pi X radius X height + 2 X pi X radius squared
51
How do ylu work out the volume of a prism
Cross sectional area x length
52
How do you work out the volume of a sphere
4/3 X pi X radius cubed
53
How do you work out the volume of a pyramid
1/3 X base area X vertical height
54
How do you work out the volume of a cone
1/3 X pi X radius squared X vertical height
55
What's the volume of a hemisphere (half a sphere)
2/3 X pi X radius cubed
56
What's a frustum of a cone
What's left when top part of a cone is cut off parallel to its circular base
57
How do you calculate the volume of a frustum
Volume of original cone - Volume of removed cone 1/3pi X radius^2 - 1/3pi X pi^2 X height
58
What's 1 litre equivalent
1000cm^3
59
What's rate of flow
Litres per minute
60
If the scale factor is n and a shape is enlarged how do things change
Sides are n times bigger Scale factor N= new length divided old length Areas are n^2 times bigger Scale factor N^2 = new area divided by old area volumes are n^3 times bigger Scale factor N^3= new volume divided by old volume
61
What's front elevation
The view you would see directly in front
62
What's plan view
View from directly above
63
What's side elevation
The view youd see from directly to one side
64
How do you construct a triangle
Draw a base line to size needed and label ends a and b Set compass to needed lengths - draw an arc Where arcs cross is point c and draw up lines to make a triangle
65
How do you construct a triangle with specific angles
Draw base line, use protractor to measure needed angle and draw up lines to make a triangle
66
What's a locus
A line or region that shows all the points which fit a given rule
67
Tell me about locus from a fixed distance from a given point
1) the locus of points which are a fixed distance from a given point Locus is just a circle
68
Tell me about the locus of points which are a fixed distance from a given line
It looks like a sausage shape Has straight sides and perfect semi circle ends
69
Tell me about the locus of points which are equidistant from 2 given lines
Keep the compass Setting the same while ylu make 4 lines Make sure you leave your compass marks showing You will get 2 equal angles this locus is also an angle bisector
70
Tell me about the locus of points which are equidistant from two given points
This locus is all points which are same distance from a as b The locus is actually the perpendicular bisector of the line joining the two points
71
How do you construct 60 degree angle with no protractor
Make an initial line, make same distance and make arcs away from it, make arc on initial line to, then on that arc draw another arc to cross over the other Where the arcs cross are where to draw other line for 60 degree angle
72
How do you construct 90 degree angles
Make an initial line, draw two arcs either side same distance away From those arcs make an arc towards the middle of the line Where the arcs cross is 90 degrees
73
How do you draw the perpendicular from a point to a line
Not quite the same as constructing 90 degree angle You will be given line do same as 90 degrees by make line longer so it's like a cross not two Ls
74
What does from mean in bearings
Put pencil on diagram at the point you are going from
75
What's the north line in bearings
At the point you going from, draw in a north line
76
What's clockwise in bearings
Now draw in the angle clockwise from north line to the line joining the two points This angle is bearing required
77
Tell me a key thing about bearings
Written in 3 digits eg not 45 degrees 045 degrees

Maths (7 decks)

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