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
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
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)
