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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
Q

What’s congruence

A

If two shapes are congruent, they are the same size and shape

They could be reflected or rotated

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26
Q

How do you prove two triangles are congruent

A

Show one of the 4 conditions (next questions)

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27
Q

What’s SSS

A

Where three sides are the same

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28
Q

What’s AAS

A

Two angles and a corresponding side match up

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29
Q

Tell me about SAS

A

Two sides and the angle between them match up

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30
Q

Tell me about RHS

A

A right angle, the hypotenuse and one other side all match up

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31
Q

What are similar shapes

A

They are the same shape but are different sizes

32
Q

Tell me how triangles can be similar

A

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
Q

Tell me about the translation transformation

A

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
Q

Tell me about the rotation transformation

A

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
Q

Tell me about reflections

A

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
Q

Tell me about enlargements

A

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
Q

Tell me the key facts of scale factors

A

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
Q

How do you work out the area of a triangle

A

1/2 X b X h (vertical height)

39
Q

How do you calculate the area of a parallelogram

A

B X h (vertical height)

40
Q

How do you calculate the area of trapezium

A

1/2(a + b) X h (vertical height)

A = opposite side of base

41
Q

How do you calculate the area of circle

A

Pi X r^2

42
Q

How do you calculate circumference

A

Pi X diameter

43
Q

How do you work out the area of a sector (area of a circle)

A

X divided by 360 x area of full circle

X = angle

44
Q

How do ylu work out the length of an arc

A

X/360 X circumference of full circle

45
Q

What does exact area mean

A

Leave answer in terms of pi for circles eg 3 pi

46
Q

What’s are vertices / a vertex

A

Corners

47
Q

What’s surface area

A

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
Q

What’s the surface area of a sphere

A

4 X pi X radius squared

49
Q

How do you work out the surface area of a cone

A

Pi X radius X slant height + pi X radius squared

50
Q

How do you work out the surface area of a cylinder

A

2 X pi X radius X height + 2 X pi X radius squared

51
Q

How do ylu work out the volume of a prism

A

Cross sectional area x length

52
Q

How do you work out the volume of a sphere

A

4/3 X pi X radius cubed

53
Q

How do you work out the volume of a pyramid

A

1/3 X base area X vertical height

54
Q

How do you work out the volume of a cone

A

1/3 X pi X radius squared X vertical height

55
Q

What’s the volume of a hemisphere (half a sphere)

A

2/3 X pi X radius cubed

56
Q

What’s a frustum of a cone

A

What’s left when top part of a cone is cut off parallel to its circular base

57
Q

How do you calculate the volume of a frustum

A

Volume of original cone - Volume of removed cone

1/3pi X radius^2 - 1/3pi X pi^2 X height

58
Q

What’s 1 litre equivalent

A

1000cm^3

59
Q

What’s rate of flow

A

Litres per minute

60
Q

If the scale factor is n and a shape is enlarged how do things change

A

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
Q

What’s front elevation

A

The view you would see directly in front

62
Q

What’s plan view

A

View from directly above

63
Q

What’s side elevation

A

The view youd see from directly to one side

64
Q

How do you construct a triangle

A

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
Q

How do you construct a triangle with specific angles

A

Draw base line, use protractor to measure needed angle and draw up lines to make a triangle

66
Q

What’s a locus

A

A line or region that shows all the points which fit a given rule

67
Q

Tell me about locus from a fixed distance from a given point

A

1) the locus of points which are a fixed distance from a given point

Locus is just a circle

68
Q

Tell me about the locus of points which are a fixed distance from a given line

A

It looks like a sausage shape

Has straight sides and perfect semi circle ends

69
Q

Tell me about the locus of points which are equidistant from 2 given lines

A

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
Q

Tell me about the locus of points which are equidistant from two given points

A

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
Q

How do you construct 60 degree angle with no protractor

A

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
Q

How do you construct 90 degree angles

A

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
Q

How do you draw the perpendicular from a point to a line

A

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
Q

What does from mean in bearings

A

Put pencil on diagram at the point you are going from

75
Q

What’s the north line in bearings

A

At the point you going from, draw in a north line

76
Q

What’s clockwise in bearings

A

Now draw in the angle clockwise from north line to the line joining the two points

This angle is bearing required

77
Q

Tell me a key thing about bearings

A

Written in 3 digits eg not 45 degrees

045 degrees

Maths (7 decks)

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