Advanced I Geometry, Coordinate Geometry, and Measurement, shape and space (7-9 old curriculum) Flashcards
radius
The measurement from the centre of a circle to any point on the circumference of that circle
diameter
The measurement of the line passing through the centre of the circle having two endpoints on the circumference of the circle.
equation to relate diameter to radius
2r = d
where r is the radius and d is the diameter of the circle
What is the circumference of a circle?
Represented by C, the circumference is the perimeter of a circle. We do not use circumference to refer to the perimeter of any other object.
C = πd
Where π is equal to a constant number that is approximately 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679
Or more approximately π = 3.14 and π is known as “pi”
And where d = diameter of the circle
Someone more brilliant came up with the number for π. The proof of this is beyond what I know at the moment. Some people find it fun to have contests to see who can memorize the most digits of pi. Go ahead and try to get a few of them memorized, but fear not, as there is a button on your calculator that will give you enough digits to be precise enough in your math homework.
Some teachers tell their students to use just 3.14 in their homework since they do not yet have calculators with the button pi. This is acceptable in junior high, but you should start using the pi button as soon as you can since it will give you more precise measurements. The pi button in the calculator is also an approximation but it is less approximate than 3.14 :)
What is the area of a circle?
A = πr^2
area of the circle = π x r x r
Find the exponent button on your calculator and learn how to use it.
Make sure that you know how to solve for r in the case that you are given the area. Hint: you will need to use a square root of both sides of the equation at some-point as you solve for r but it is not the first step.
bisector
something that splits the other thing into 2 (divides it by 2)
Know how to draw a perpendicular line segment given another line
There are various ways, best shown to you first by a teacher, but here is a summary:
- Use a compass (compass = point on one side, pencil on the other) and straight-edge: draw a bit of a circumference of the same radius from the endpoints of the original line segment, making sure to get the two intersection points of those two circles you are drawing - this gets you the perpendicular bisector so it also splits your original line in two
- Use a protractor: find 90 degrees and draw a line that is at that angle; this does not split the original line in two and allows you to put the new line anywhere
- Use a right triangle (triangle with a 90 degree angle) and put one of the legs on the original line, the other leg is the perpendicular (leg is the name for a side length on a triangle that is not the hypotenuse; the hypotenuse is the longest side of a right triangle)
Know how to draw a parallel line segment given another line
There are various ways, best shown to you first by a teacher, but here is a summary:
- use a compass and using the same radius draw many different circumferences (plural of radius) at a few different spots along the line (so put the pointy end on the original line and draw a circle), then draw a line passing through just one point of each of the circles making sure to never cross the original line. For accuracy it is best to draw these circles far away from each other and to have three instead of just two circles.
- If you just need a parallel line but do not need it to be in a certain place, just put your ruler up to the old line and draw the new line on the other side of the ruler
- You can also construct a parallel line by using the method to construct a perpendicular line, but just do this twice. That way the first line and the third line will be parallel to each other but your second line will be perpendicular to the first and third line.
Know how to draw an angle bisector given an angle
There are various ways, best shown to you first by a teacher, but here is a summary:
- Use a compass to draw a circle with the vertex of the angle as the centre of the circle. Then lift your compass and draw two more circles one centred on each of the intersections you just created. Where these two new circles meet is where you have to pass through with your angle bisector. This also should pass through the vertex of your angle.
- measure the original angle with your protractor and then divide by two to get the resulting angle bisector.
What are the four quadrants on the Cartesian plane?
Quadrant 1: where x and y are both positive (top right)
Quadrant 2: top left
Quadrant 3: bottom left
Quadrant 4: bottom right
Best to just memorize that quadrant 1 is top right, then go counterclockwise to get the others
Remember that the Cartesian plane is just two number lines put together perpendicular to each other with the positive side of the number line going to the right for one of the lines, and up for the other number line.
What is the Pythagorean Theorem?
a^2 + b^2 = h^2
Where a is one leg of a right triangle, b is the other leg of a right triangle, and h is the hypotenuse (the longest side length of a right triangle).
To solve for any of these variables you will need a good knowledge of square rooting since all of these have an exponent 2. Use preservation of equality to ensure that you are keeping the equals sign truthful.
This theorem is used to solve for a missing side length in a right triangle only, and does not work if there is not a 90 degree angle in the triangle!
How do you determine the surface area of a right rectangular prism?
SA = 2lw + 2wh + 2lh since you must add the areas of each of the rectangles in the net of the shape. Also the 2 is showing that there are two sides that are the same.
You can make this formula easier to enter in your calculator like this:
Factor out the 2 and multiply by it at the end:
SA = 2 (lw +wh + lh)
where l = length
w = width
h = height
How do you determine the surface area of a right triangular prism?
notice in the image that they have a different orientation than what is perhaps presented elsewhere, and you must always define your variables!
This is seen as one huge rectangle that is folded over to make 3 smaller rectangles. The formula is there to make everything easier, but you must understand where it comes from. If you prefer you can add the area of two triangles and three rectangles.
You may need to use Pythagorean theorem to find some of the triangle information such as s1. s2, s3 or h.
Your teacher will likely show you which type of right triangular prism they will have you work with, but they may expect you to work with any type. There is no set way to answer these questions since it depends on what you are given. This is where conceptual understanding tends to triumph over memorized procedures. Use symmetry wherever possible to reduce your work and chance of error.
How do you determine the surface area of a right cylinder?
right cylinder area = area of the two identical circles plus the area of a rectangle
You may need to use the circumference of a circle formula to get one of the side lengths of your rectangle. This may mean that you also may have to use the formula that compares a radius to a diameter as well. Make sure you know all the cards prior to this one in the decks to have success.
net
Shows the 3D object as it would look like if opened and flattened in 2D
Nets are useful when you are trying to calculate surface areas of 3D objects since you can keep track of what areas you have calculated.
