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maths > Geometery > Flashcards

Geometery Flashcards

1
Q

Rules for congruent triangles

A

sss
sas
aas
rhs
(aaa)

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2
Q

parallelogram vs rhombus

A

parallelogram = tilted rectangle
rhombus = tilted square

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3
Q

What do the s, a, r and h mean in the rules for congruent triangles?

A

s = side
a= angle
r= right angle
h= hypotenuse

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4
Q

polygon

A

A closed 2D shape with only straight sides.

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5
Q

What do we consider a regular polygon?

A

A polygon where all of its sides are the same length and all its angles are the same size.

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6
Q

How many lines of symmetry do regular polygons have?

A

It’s the same as the number of sides.

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7
Q

What order of rotational symmetry do regular polygons have?

A

It’s the same as the number of sides.

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8
Q

What do we mean by congruent shapes?

A

Shapes of identical shape and size.

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9
Q

area of a trapezium?

A

A = 1/2 (a+b) h

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10
Q

curved surface area of a cone formula

A

πrl

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11
Q

volume of a cone formula

A

1/3 π r² h

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12
Q

How many pairs of parallel sides does a kite have?

A

0

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13
Q

How many lines of symmetry does a trapezium have?

A

0

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14
Q

What must the internal angles of a quadrilateral add up to?

A

360°

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15
Q

What feature must be identical for two shapes to be considered similar?

A

Their shape

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16
Q

To confirm that two shapes are similar, what can we do?

A

Check that all of the angles are the same size.

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17
Q

When discussing shapes, do the terms ‘similar’ and ‘mathematically similar’ mean the same thing?

A

Yes

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18
Q

what does h stand for?

A

Perpendicular height

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19
Q

Area of a rectangle?

A

A = l x w

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20
Q

Area of a parallelogram?

A

A = b x h

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21
Q

Area of a triangle?

A

A = 1/2 x b x h

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22
Q

What is a chord?

A

A straight line which connects two points on the circumference of a circle.

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23
Q

What is a segment?

A

The two parts of a circle when a chord splits it in two.

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24
Q

What is the minor segment?

A

The smaller segment.

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25
Q

What is the major segment?

A

The larger segment.

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26
Q

What is an arc?

A

A section of a circle’s circumference.

(the smaller is the minor arc and the larger is the major arc)

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27
Q

What is a sector?

A

A section of a circle as if you’ve cut a piece of cake.

Involves two radii which each go from the centre of the circle to the circumference, joined by an arc.

There are two - major and minor.

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28
Q

Length of an arc formula?

A

x/360 x 2πr

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29
Q

Area of a sector formula?

A

x/360 x πr²

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30
Q

How many edges does a cube have?

A

12

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31
Q

How many faces does a cube have?

A

6

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32
Q

How many vertices does a cube have?

A

8

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33
Q

How many vertices does a sphere have?

A

0

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34
Q

How many faces does a sphere have?

A

1

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35
Q

How many edges does a sphere have?

A

0

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36
Q

How many vertices does a cylinder have?

A

0

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37
Q

How many edges does a cylinder have?

A

2

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38
Q

How many faces does a cylinder have?

A

3

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39
Q

How many vertices does a cone have?

A

1

40
Q

How many edges does a cone have?

A

1

41
Q

How many faces does a cone have?

A

2

42
Q

Volume of a sphere formula

A

4/3 π r³

43
Q

Volume of a hemisphere formula

A

2/3 π r³

44
Q

Volume of a cylinder formula

A

area of the cross-section x length

45
Q

Volume of a prism formula

A

area of the cross-section x length

46
Q

Volume of a cone formula

A

1/3 π r² h

47
Q

Volume of a pyramid formula

A

1/3 x base area x vertical height

48
Q

What do the angles in a triangle add up to?

A

180°

49
Q

What do the angles on one side of a straight line add up to?

A

180°

50
Q

What do the angles in a quadrilateral add up to?

A

360°

51
Q

What do the angles around a point add up to?

A

360°

52
Q

What things are the same in an isosceles triangle?

A

-Two side lengths
-Two angles

53
Q

What do we need to use the 3 more complex angle rules for?

A

Two parallel lines cut through by a transversal.

54
Q

Vertically opposite angles are…

A

equal.

55
Q

alternate angles are…

A

equal.

56
Q

corresponding angles are…

A

equal.

57
Q

What do co- interior (‘allied’) angles add up to?

A

180°

58
Q

What shape do we look for for alternate angles?

A

Z

59
Q

What shape do we look for for corresponding angles?

A

F

60
Q

What shape do we look for for co-interior angles?

A

the blocky c ( [ )

61
Q

Find the bearing basically means…

A

in what direction?

62
Q

Which direction must we measure bearings from?

A

North

63
Q

In which way should we measure bearings?

A

Clockwise (from north)

64
Q

How many digits are bearings written with?

A

3

e.g. 046°, 120°

65
Q

What symbol must follow a bearing?

A

°

66
Q

If something is ‘to scale’ then…

A

all proportions must be correct.

67
Q

What is a scale drawing?

A

A drawing to scale

68
Q

What is a scale diagram?

A

A diagram to scale e.g. a map.

69
Q

When looking at scale drawings, what should we do?

A

Measure the lines with ruler!

70
Q

How can 1:1600 also be written?

A

1cm = 1600cm

71
Q

What does the ratio 1:1600 mean in context?

A

Everything on the image is 1600x smaller than in real life.

72
Q

Make sure you convert to…

A

the correct units!!!!!

73
Q

Translation

A

moving a shape up, down, left, or right

74
Q

Rotation

A

spinning a shape by rotating it by a specified angle

75
Q

Reflection

A

flipping a shape by applying a line of reflection

76
Q

Enlargement

A

making a shape bigger or smaller by applying a scale factor

77
Q

How do we describe the movement in a translation?

A

using a vector

where x= horizontal movement (positive for right, negative for left)

y = vertical movement (positive for up, negative for down)

78
Q

How do we know if a shape has been translated?

A

-If it remains identical in size and shape

-A vector describes the movement from the original to the final position

79
Q

When describing a rotation, what must we specify?

A

-Angle of rotation

-Direction (clockwise or anticlockwise)

-Centre of rotation

e.g. rotated 90° clockwise about the centre of rotation (3,2).

80
Q

How do we know if a shape has been rotated?

A

-If the shape remains the same shape and size during rotation

-A full rotation is 360°

-You can use tracing paper to draw a rotated shape

81
Q

When describing a reflection, what must we specify?

A

-The equation of the mirror line.

e.g. The triangle has been reflected in the line x = 8

82
Q

Common mirror lines

A

y-axis (x = 0)

x-axis (y = 0)

y = x (the line at 45° through the origin)

y = -x (the line at -45° through the origin)

83
Q

How do we tell if a shape has been reflected?

A

-If a shape remains the same shape and size

-The distance from any point to the mirror line is equal to the distance from its reflection to the mirror line

-Reflections reverse orientation (e.g., left becomes right)

84
Q

When describing an enlargement, what must we specify?

A

-Scale factor

-Centre of enlargement

85
Q

What does a scale factor of 2 mean?

A

The new shape is twice as large as the original shape

86
Q

What does a scale factor of 1/4 mean?

A

The new shape is a quarter of the size of the original shape.

87
Q

What does an enlargement involve?

A

Changing the size of a shape relative to a fixed point.

88
Q

How do we calculate the scale factor (k) for an enlargement?

A

Using the ratio of corresponding sides:

k = length of side in image ÷ length of side in original

89
Q

K > 1 for an enlargement

A

shape gets larger

90
Q

what does k represent for enlargements?

A

the scale factor

91
Q

0 < k < 1 for an enlargement

A

shape gets smaller

92
Q

k < 0

A

shape is inverted (rotated 180°)

93
Q

k = -1

A

equivalent to a 180° rotation

94
Q

k = 1 (enlargement)

A

no change in size

95
Q
A

maths (7 decks)

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