Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

MAT > Geometry > Flashcards

Geometry Flashcards

1
Q

The diagonal of a square is

A

root 2 times longer than the side

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

The side of a square is

A

root 2 times shorter than the diagonal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

The height of an equilateral triangle is

A

root three times longer than half of the base

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

For circles, add

A

key radii at strategic places

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Split up the shape into

A

manageable chunks

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

for a shared length find

A

two expressions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Draw right angled triangles using radii

A

Give radii length 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Sector area =

A

0.5Xr^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Arc length =

A

rX

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Whenever one of the edges is an arc

A

one of your sub-areas will be a sector

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

When asked to find the area of a complex shape

A

split it up; there tends to be an easier way

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Nearest point from a circle means

A

draw a line from the centre of the circle to the point of interest

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Consider the conditions for which the equation of a circle area valid i.e

A

r, r^2 > 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Exterior angle =

A

360/n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Interior angle =

A

180 – 360/n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Sine rule:

A

two sides + opposite angle, one side + two angles

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Obtuse/acute

A

multiple answers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Reflect on the significance of

A

each piece of information given to you

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

We have a tangent

A

likely be able to use the alternate segment theorem

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

If two circles touch

A

we have a tangent, use alternate segment theorem

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Given the diameter

A

the angle subtended on the circumference is 90 degrees

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Use variables to represent appropriate unknown angles/lengths

A

form equations using Pythagoras or comparing lengths to find the values of these variables

23
Q

Look out for similar triangles to

A

compare lengths

24
Q

Extend or add lines where necessary

A

Justify your assumptions

25
Q

Similar triangles

A

if two triangles are similar, then their ratio of width to height is the same. They are similar if have two equal angles, two sides of equal ratio and an included angle that is equal, or if three sides of equal ratios. One common occurrence is where one triangle is embedded in the other.

26
Q

Circle theorem (5):

A

angle in semi-circle = 90 degrees,
angle in same segment is equal (2 angles subtended from the same minor arc are equal), The angles subtended by the chord at the circumference of the circle are equal.
angle between chord and tangent is equal to angle in alternate segment,
angle at circumference is half the angle at centre,
opposite angles in cyclic quadrilateral is equal to 180 degrees.

The angle subtended at the centre of a circle is double the size of the angle subtended at the edge from the same two points,
Angles which are in the same segment are equal, i.e. angles subtended (made) by the same arc at the circumference are equal,
The angles which are within a semicircle add up to 90°,
Opposite angles in a cyclic quadrilateral add up to 180°,
Alternate Segment Theorem, i.e. that the angle between a tangent and its chord is equal to the angle in the ‘alternate segment’.

27
Q

Alternate segment theorem

A

chord meets tangent

28
Q

When asked to find the area of a more complex shape

A

split it up, tends to be an easier way to do so

29
Q

Whenever one of the edges is an arc

A

one of your sub-areas will be as sector

30
Q

area of triangle with co-ordinates (0,0) (a,b) (c,d) =

A

0.5|ad-bc|

31
Q

Point on a circle a closest to circle b:

A

distance between centre;s, fraction of radii to length, times that by x and y distances, +- for correct circle’s centre

32
Q

triangle and circle –>

A

look for sectors and equal areas

33
Q

sinX , cosX in triangle

A

look for trig length (of 1)

34
Q

triangle + circle = sector

A

x + y = k
largest co-
ordinates on a circle and line

35
Q

smallest value of a circle at a certain point

A

1/root 2

36
Q

Always think how to get sinX cosX - if length is 1, look for triangles and trig

A

(sinX-cosX)^2 > 0

37
Q

x^2 + y^2 or y = -(x+7)^0.5

A

think circle

38
Q

Extreme co-ordinates

A

think how it changes the graphs

39
Q

A(k) = A(2-k) therefore

A

as even function about k=1

40
Q

Angle at circumference =

A

1/2 * angle at radius

41
Q

Sin(2a) =

A

don’t need 2sinacosa but may be useful

42
Q

Tangent to circle:

A

repeated root, (2y-3)^2 when equating line to circle as touches, one solution

43
Q

If triangle and circle think

A

of sectors, equal/repeated areas

44
Q

If an area has a pi, likely to involve

A

a sector = 0.5Xr^2

45
Q

Reflect Q(x, y) in y=mx+c to find P(x,y)

A

PQ is perpendicular to y=mx+c, find equation of PQ and equate to y to find point of intersection M –> QM = MP

46
Q

Circle inside equilateral triangle

A

area a is congruent to area b and c

47
Q

Sphere

A 
A = 4pir^2
V = 4/3 pi r^3
48
Q

Cone

A 
A = pi*r*(L+R)
V = 1/3 * pi *h *r^2
49
Q

Cylinder

A 
A = 2pi*r*(r+h)
V = pi*h*r^2
50
Q

Max of x+y when xx + yy <=1

A

the inequality means it lies on or inside the circle
let x+y = c then y=c-x, as c increases it shifts this line upwards until it becomes a tangent to the circle and x+y = root 2

51
Q

Use variables for lengths

A

s

52
Q

Area of trapezium =

A

0.5h(a+b)

53
Q

Point that splits P(2,3) and Q(8,-3) in ration 1:2

A

Difference of PQ is (6,-6) is and so we want to add (2, -2) to P or subtract (4, -4) from Q to get (4, 1)

54
Q

R is a reflection of P in x axis and so if X is a point on the x axis then PX = RX,

A

if S is a reflection of Q in the line y=mx+c then if Y is a point on that line then QY = YS

MAT (14 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions