Section 5 - Geometry And Measures Flashcards
Tell me the 5 simple rules of geometry
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
Tell me about angles around parallel lines
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
Tell me about alternate angles
Alternate angles are the same and found in a Z shape
Tell me about allied/ interior angles
Allied angles add to 180 and found in a c or u shape
Tell me about corresponding angles
They are the same, found in an f shape
What’s 3 letter notation
Eg angle abc is referring angle formed at b - might see it as b with a little hat
What’s a polygon
Can be regular or irregular
A regular polygon is where all the sides and angles are the same
List some regular polygon names
Equilateral triangle Square Pentagon Hexagon Heptagon Octagon Nonagon Decagon
What are the sum of exterior angles in a polygon
For any polygon
360 degrees
How do you work out the sum of interior angles in a polygon
For any polygon
(N - 2) X 180
N= number of sides
How do you work out an exterior angle of a regular polygon
360 divided by n (number of sides)
How do you work out the interior angles in a regular polygon
180 - exterior angle
Tell me about equilateral triangles
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)
Tell me about right angled triangles
1 right angle
No lines of symmetry
No rotational symmetry
Tell me about isosceles triangles
2 sides are the same
2 angles the same
1 line of symmetry
No rotational symmetry
Tell me about scalene triangles
All 3 different sides
All three different angles
No symmetry
Tell me about squares
4 equal angles
4 lines lf symmetry
Rotational symmetry order 4
Diagonals are the same length and cross at right angles
Tell me about rectangles
4 equal angles
2 lines of symmetry
Rotational symmetry order of 2
Tell me about rhombus
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
Tell me about parallelogram
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
Tell me about trapezium
1 pair of parallel sides
No lines of symmetry
No rotational symmetry
Tell me about kites
2 pairs of equal sides
1 pair of equal angles
1 line of symmetry
No rotational symmetry
Diagonals cross at right angles
Tell me the rules of a circle
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
Tell me about the alternate segment theorem
The angle between a tangent and a chord is always equal to the angle in the opposite segment
What’s congruence
If two shapes are congruent, they are the same size and shape
They could be reflected or rotated
How do you prove two triangles are congruent
Show one of the 4 conditions (next questions)
What’s SSS
Where three sides are the same
What’s AAS
Two angles and a corresponding side match up
Tell me about SAS
Two sides and the angle between them match up
Tell me about RHS
A right angle, the hypotenuse and one other side all match up
What are similar shapes
They are the same shape but are different sizes
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
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)
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
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
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)
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
How do you work out the area of a triangle
1/2 X b X h (vertical height)
How do you calculate the area of a parallelogram
B X h (vertical height)
How do you calculate the area of trapezium
1/2(a + b) X h (vertical height)
A = opposite side of base
How do you calculate the area of circle
Pi X r^2
How do you calculate circumference
Pi X diameter
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
How do ylu work out the length of an arc
X/360 X circumference of full circle
What does exact area mean
Leave answer in terms of pi for circles eg 3 pi
What’s are vertices / a vertex
Corners
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
What’s the surface area of a sphere
4 X pi X radius squared
How do you work out the surface area of a cone
Pi X radius X slant height + pi X radius squared
How do you work out the surface area of a cylinder
2 X pi X radius X height + 2 X pi X radius squared
How do ylu work out the volume of a prism
Cross sectional area x length
How do you work out the volume of a sphere
4/3 X pi X radius cubed
How do you work out the volume of a pyramid
1/3 X base area X vertical height
How do you work out the volume of a cone
1/3 X pi X radius squared X vertical height
What’s the volume of a hemisphere (half a sphere)
2/3 X pi X radius cubed
What’s a frustum of a cone
What’s left when top part of a cone is cut off parallel to its circular base
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
What’s 1 litre equivalent
1000cm^3
What’s rate of flow
Litres per minute
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
What’s front elevation
The view you would see directly in front
What’s plan view
View from directly above
What’s side elevation
The view youd see from directly to one side
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
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
What’s a locus
A line or region that shows all the points which fit a given rule
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
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
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
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
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
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
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
What does from mean in bearings
Put pencil on diagram at the point you are going from
What’s the north line in bearings
At the point you going from, draw in a north line
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
Tell me a key thing about bearings
Written in 3 digits eg not 45 degrees
045 degrees
