1.3 Geometry Flashcards
In relation to a triangle what is a vertex?
The point where two sides meet
How are equal sides shown on a triangle?
By a dash or double dash
How are equal angles shown in a triangle?
By an arc or double arc in the corner with no number
What is an obtuse triangle?
When one angle is greater than 90°
What is the long side of a right angle triangle called?
Hypotenuse
What is a scalene triangle?
When all three sides and all three angles are different values
In writing what is Pythagoras theorem?
The area of the square on the hypotenuse is equal to the sum of areas on the other two sides?
What is the formula for Pythagoras theorem?
a^2 + b^2 = c^2
What can be used to find the height of a equilateral and isosceles triangle?
Pythagoras theorem
If you have an unknown angle but know the radius and arc length what is the formula to work out the angle?
Arc length over radius
What is an acute angle?
Less than 90°
What is a right angle?
When a angle is exactly 90°
What is an obtuse angle?
When a angle is between 90° and 180°
What is a reflex angle?
When a angle is greater than 180°
What is a complementary angle?
When multiple angles add up to 90°
What is a supplementary angle?
When angles add up to 180°
What is a supplementary angle?
When angles add up to 180°
What is a vertical angle?
When two opposite angles on two intersecting lines have the same degree measurement
What is a alternate interior and a alternate exterior angle?
When you have two parallel lines with a line crossing both. The angles on the inside and outside will be the same
What is a angle bisector?
A line that splits an angle into two equal angles
On a graph what is the dependent variable?
The value that depends on other allocated values
On a graph what is the independent value?
When a value can be any value it wants with nothing else affecting it
What is the point where the x axis and y axis on a graph meet called?
The origin
What is the definition of a straight line?
As a short distance between two points
What is the equation of a straight line?
Y=mx+c
What does m represent in the straight line equation?
Gradient of the line
What does the c represent in a straight line equation on a graph? I.e y=mx+c or y=3x+1
The point in which the line crosses the y axis
In a straight line equation what is represented by the mx in the equation? i.e y=mx+c or y=3x+1
When the value of x increase the value of y increases by that value. I.e when x increases by 1 the y increases by 3
In a straight line graph if you aren’t given a c value what must you take it as? i.e y=2x
The line crosses the y axis at the 0 point
On a straight line graph what happens if you aren’t given a x value? I.e y=5
Then it will be parallel horizontal line passing through the given y axis
On a straight line graph what happens if you aren’t given a c value and it says x=(any number)? I.e x=3
It will be parallel vertical line passing through the x axis at the given value
If you’re given two coordinates for a straight line graph and told to find the equation what must you do? I.e (1,4)(3,10)
Substitute the values into the straight line formula y=mx+c then solve as a simultaneous equation. I.e 4=1m+c and 10=3m+c
When plotting a quadratic equation onto a graph what shape will it make? I.e 6x^2+3x+3
A smooth symmetrical curve
When plotting a quadratic equation on a graph which way will it face if the first coefficient is positive?
Open end up
When plotting a quadratic equation on a graph which way will it face if the first coefficient is negative?
Open end downwards
When plotting a quadratic equation on a graph having a larger number on your first coefficient makes the graph?
Narrower
When plotting a quadratic equation on a graph what does your last value indicate?
The y axis intercept
What are the roots of a quadratic equation on a graph?
The values at which it crosses the x axis
What is the adjacent side of a right angle triangle?
It is the non-hypotenuse side that is next to a given angle
What is the opposite side of a right angle triangle?
The side across from a given angle
What do all interior angles of a triangle add up to?
180°
What is trigonometry?
A branch of maths that studies the relationship between sides lengths and angles of triangles
What method is used in trigonometry to remember sine, cosine, tangent?
SOHCAHTOA
Sine=opposite/ hypotenuse
Cosine = adjacent/ hypotenuse
Tangent= opposite/ adjacent
On a graph what is the horizontal axis called?
The x axis
On a graph what is the vertical axis called?
The y axis
How are rectangular coordinates represent?
(X,Y) along then up or down
How are polar coordinates represented?
(R,θ) length, theta
What is theta? θ
A sign that is given to an unknown angle
When plotting polar coordinates on your graph what does a positive theta mean?
It goes anticlockwise from the origin-x axis
When plotting polar coordinates on your graph what does a negative theta mean?
It goes clockwise from the origin-x axis
