Section 5 - Geometry Flashcards
Isosceles triangles have
2 same sides and 2 same angles
Where are alternate angles formed
In a z shape
Where are corresponding angles formed
In an f shape
Where are allied angles formed
In a c / u shape
Allied angles
Add to 180
Sum of exterior angles in a polygon =
360
For any polygon interior angle =
180 - exterior angle
In a rhombus/ parallelo
Opposite angles are equal and neighbouring angles add to 180
First circle rule
A tangent and radius meet at 90 degress
Second rule for circles
Two radii form a isosceles triangle
Third circle theorem
The perpendicular bisector of a chord passes through the centre of the circle
Fourth circle theorem
Angle at the centre is twice angle at circumference
Fifth circle theorem
Angle in semicircle is 90 degrees
Sixth circle theorem
Angles in same segment are equal
7th circle theorem
Opposite angles in a cyclic quadrilateral add to 180
8th circle theorem
Tangents from the same point are the same length
9th circle theorem
Angle between a tangent and chord is always equal to the angle in the opposite segment
Congruent
Same size and shape
Name the 4 ways to prove a triangles congruent
Sss
Aas
Sas
Rhs
Similar
Same shape different size
Two triangles are similar if
All angles match up
All sides proportional
2 sides proportional and angle between is the same
How to write a vector
(X over y)
X is the horizontal
Y is the vertical
When do you use vectors
For translations
What 3 details must you give for rotations
Angle of rotation
Direction of rotation
Centre of rotation
What 2 details must you mention in enlargements
Scale factor
Centre of enlargement
What happens when a scale factor is negetive
The shape moves to other side of centre of enlargement
Area of a trapezium
Average of parallel sides x vertical height
Area of sector
X ÷ 360 times area of full circle
Ark length
X ÷ 360 x circumference of circle
Surface area of cone
Pi x radius x slanted height
Surface area of cylander
(2 x pi x radius x height) + ( 2 x pi x r²)
Volume of cylinder
Pi x r² x height
Volume of prism
Cross sectional area x length
Volume of pyramid
1/3 × base area × vertical height
Volume of cone
1/3 × pi r² × vertical height
What is a frustum of a cone
What’s left when the top part of cone is cut off
Volume of frustum
Volume of origional cone - volume of removed cone
How does enlargement effect area and volume?
For a scale factor of n
The sides are n times bigger
The areas n² times bigger
The volumes n³ times bigger
What is the front elevation
The view from the front
What is the side elevation
View from one side
What is the plan
The view you see from above
What is a locus
A line or region that shows all the points which fit a given rule
Type 1 of loci
Points are a fixed distance from a given point.
A circle
Type 2 of loci
Points are a fixed distance from a given line
A sausage shape
Type 3 of loki
Points are an equal distance from 2 given lines.
Line through the middle
Type 4 loki
Points which are an equal distance from 2 given points
How to plot a bearing
Find the word from in the question and put your pencil at that point
Draw a North line
Draw in the angle clockwise to the north angle
