The Pythagorean Theorem Flashcards
The longest side of a right triangle, opposite the right angle, is called ____
the hypotenuse
The other two sides are called the ____
legs (or adjacent and opposite, in trigonometry)
The Pythagorean formula is ____
Every positive number has how many square roots?
two, a positive and negative
The symbol √ is called the ____
radical sign / radical symbol, meaning the principal square root (the positive one)
Sometimes a calculator gives you an answer like this to a Pythagoras question. What kind of form is this in?
simplified surd form / simplified radical form
(if you want to get it back to an unsimplified form, square the number outside the root and multiply it by the number inside (eg. 4x4=16, 16x5=80)
Arrange the Pythagorean formula to solve for the hypotenuse
Arrange the Pythagorean formula to solve for one of the shorter sides, leg (a)
In this radical, the 5 is the ____
coefficient
In this radical, the 4 is the ____
index or degree
In this radical, the 13 is called the ____
radicand
The square root of x is the same as x to the power ____
1/2
because when you multiply powers, you add the exponents, so 9^1/2 * 9^1/2 = 9^1 or √9 * √9 = 9
The cube root of x is the same as x to the power ____
1/3
Sets of three positive whole numbers (natural numbers) that fit the Pythagorean formula are called ____
eg. 3, 4, 5
eg. 6, 8, 10
Pythagorean triples
Two lines that intersect (meet) at a right angle are called ____
perpendicular lines
To find the area of a triangle ____
multiply the base (any side) by its perpendicular height, then divide by 2
To find the area of a circle, ____
find the radius (or half the diameter), square it and multiply by pi
The distance from one side of the circle or sphere to the opposite side, passing through the center is called the ____
diameter
The distance from the center of a circle or sphere to its perimeter / circumference is called the ____
radius
How do you find the volume of a prism or cylinder?
Find the cross sectional area and multiply by the length
How do you find the volume of a pyramid or cone?
Find the area of the base, multiply by the height and divide by 3
What is the difference between the lateral surface area and the total surface area of a solid?
(“solid” is another name for 3D shape)
Total surface area = the sum of the area of all faces, including the base(s)
Lateral surface area = the area of all faces, excluding the base(s)
How do you find the volume of a sphere?
Cube the radius, multiply by 4, divide by 3, multiply by pi
Why do some questions ask you to give an approximate value for your answer?
because it expects you to round your answer, so it won’t be perfectly accurate
What’s the difference between accuracy and precision?
Precise: close to other points, eg. a ruler with mm is more precise than a ruler with only cm
Accurate: close to the true value, eg. a ruler made of metal is best for measuring something made of metal (because different materials change size in different ways depending on the temperature)
If you have to calculate something with pi (or any other irrational number), how do you avoid losing accuracy?
Leave your answers in terms of pi, or as square roots (surd form), while you are doing the calculations and only round it when you are at the end of the question
or
Put everything into the calculator in one single formula
(unless the question asks you to use 3.14 instead of pi)
A shape that is composed of two or more geometric shapes is called a ____
compound / composite shape
