Geometery Flashcards
Rules for congruent triangles
sss
sas
aas
rhs
(aaa)
parallelogram vs rhombus
parallelogram = tilted rectangle
rhombus = tilted square
What do the s, a, r and h mean in the rules for congruent triangles?
s = side
a= angle
r= right angle
h= hypotenuse
polygon
A closed 2D shape with only straight sides.
What do we consider a regular polygon?
A polygon where all of its sides are the same length and all its angles are the same size.
How many lines of symmetry do regular polygons have?
It’s the same as the number of sides.
What order of rotational symmetry do regular polygons have?
It’s the same as the number of sides.
What do we mean by congruent shapes?
Shapes of identical shape and size.
area of a trapezium?
A = 1/2 (a+b) h
curved surface area of a cone formula
πrl
volume of a cone formula
1/3 π r² h
How many pairs of parallel sides does a kite have?
0
How many lines of symmetry does a trapezium have?
0
What must the internal angles of a quadrilateral add up to?
360°
What feature must be identical for two shapes to be considered similar?
Their shape
To confirm that two shapes are similar, what can we do?
Check that all of the angles are the same size.
When discussing shapes, do the terms ‘similar’ and ‘mathematically similar’ mean the same thing?
Yes
what does h stand for?
Perpendicular height
Area of a rectangle?
A = l x w
Area of a parallelogram?
A = b x h
Area of a triangle?
A = 1/2 x b x h
What is a chord?
A straight line which connects two points on the circumference of a circle.
What is a segment?
The two parts of a circle when a chord splits it in two.
What is the minor segment?
The smaller segment.
What is the major segment?
The larger segment.
What is an arc?
A section of a circle’s circumference.
(the smaller is the minor arc and the larger is the major arc)
What is a sector?
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.
Length of an arc formula?
x/360 x 2πr
Area of a sector formula?
x/360 x πr²
How many edges does a cube have?
12
How many faces does a cube have?
6
How many vertices does a cube have?
8
How many vertices does a sphere have?
0
How many faces does a sphere have?
1
How many edges does a sphere have?
0
How many vertices does a cylinder have?
0
How many edges does a cylinder have?
2
How many faces does a cylinder have?
3
How many vertices does a cone have?
1
How many edges does a cone have?
1
How many faces does a cone have?
2
Volume of a sphere formula
4/3 π r³
Volume of a hemisphere formula
2/3 π r³
Volume of a cylinder formula
area of the cross-section x length
Volume of a prism formula
area of the cross-section x length
Volume of a cone formula
1/3 π r² h
Volume of a pyramid formula
1/3 x base area x vertical height
What do the angles in a triangle add up to?
180°
What do the angles on one side of a straight line add up to?
180°
What do the angles in a quadrilateral add up to?
360°
What do the angles around a point add up to?
360°
What things are the same in an isosceles triangle?
-Two side lengths
-Two angles
What do we need to use the 3 more complex angle rules for?
Two parallel lines cut through by a transversal.
Vertically opposite angles are…
equal.
alternate angles are…
equal.
corresponding angles are…
equal.
What do co- interior (‘allied’) angles add up to?
180°
What shape do we look for for alternate angles?
Z
What shape do we look for for corresponding angles?
F
What shape do we look for for co-interior angles?
the blocky c ( [ )
Find the bearing basically means…
in what direction?
Which direction must we measure bearings from?
North
In which way should we measure bearings?
Clockwise (from north)
How many digits are bearings written with?
3
e.g. 046°, 120°
What symbol must follow a bearing?
°
If something is ‘to scale’ then…
all proportions must be correct.
What is a scale drawing?
A drawing to scale
What is a scale diagram?
A diagram to scale e.g. a map.
When looking at scale drawings, what should we do?
Measure the lines with ruler!
How can 1:1600 also be written?
1cm = 1600cm
What does the ratio 1:1600 mean in context?
Everything on the image is 1600x smaller than in real life.
Make sure you convert to…
the correct units!!!!!
Translation
moving a shape up, down, left, or right
Rotation
spinning a shape by rotating it by a specified angle
Reflection
flipping a shape by applying a line of reflection
Enlargement
making a shape bigger or smaller by applying a scale factor
How do we describe the movement in a translation?
using a vector
where x= horizontal movement (positive for right, negative for left)
y = vertical movement (positive for up, negative for down)
How do we know if a shape has been translated?
-If it remains identical in size and shape
-A vector describes the movement from the original to the final position
When describing a rotation, what must we specify?
-Angle of rotation
-Direction (clockwise or anticlockwise)
-Centre of rotation
e.g. rotated 90° clockwise about the centre of rotation (3,2).
How do we know if a shape has been rotated?
-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
When describing a reflection, what must we specify?
-The equation of the mirror line.
e.g. The triangle has been reflected in the line x = 8
Common mirror lines
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)
How do we tell if a shape has been reflected?
-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)
When describing an enlargement, what must we specify?
-Scale factor
-Centre of enlargement
What does a scale factor of 2 mean?
The new shape is twice as large as the original shape
What does a scale factor of 1/4 mean?
The new shape is a quarter of the size of the original shape.
What does an enlargement involve?
Changing the size of a shape relative to a fixed point.
How do we calculate the scale factor (k) for an enlargement?
Using the ratio of corresponding sides:
k = length of side in image ÷ length of side in original
K > 1 for an enlargement
shape gets larger
what does k represent for enlargements?
the scale factor
0 < k < 1 for an enlargement
shape gets smaller
k < 0
shape is inverted (rotated 180°)
k = -1
equivalent to a 180° rotation
k = 1 (enlargement)
no change in size
