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Old - Pythagorean Theorem & Irrational Numbers
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Vocabulary that you need to know for the Looking For Pythagoras unit / common core standards
Terms in this set (24)
Triangle
A three sided polygon in which the sum of the interior angles is 180⁰.
Right Triangle
A triangle with one 90⁰ angle.
Legs
The sides of a right triangle that are adjacent to the right angle (i.e. they meet at a 90° angle)
Square Root
(a) NUMERIC DEFINITION: What number multiplied by itself is equal to the value being "rooted"? Example: √16 = 4 because 4×4=16. (b) GEOMETRIC DEFINITION: If the area of a square is A, the side length of the square it √A. For example, if the area of a square is 10, the length of the side of the square is √10.
Irrational Number
A number that cannot be written as a fraction of two integers. As decimals, they are non-terminating AND non-repeating.
Acute Triangle
A triangle with three acute angles (angles that are less than 90⁰).
Cube Root
(a) NUMERIC DEFINITION: A number when multiplied by itself 3 times gives the value. Example: ³√8 = 2 because 2×2×2=8. (b) GEOMETRIC DEFINITION: The side length of a cube that has that number as its volume.
Hypotenuse
The side of a right triangle that is opposite the right angle and is the triangle's longest side.
Obtuse Triangle
A triangle that has one angle with a measure greater than 90⁰.
Perpendicular
A straight line at an angle of 90 degrees to a given line, plane or surface.
Pythagorean Theorem
If a triangle is a right triangle, then the sum of the squares of the two legs (shortest sides) of a right triangle is equal to the square of the triangle's hypotenuse (i.e. a² + b² = c², where a & b are the legs and c is the hypotenuse)
Rational Number
A number that can be written as a fraction of two integers. As a decimal, it is either terminating or repeating.
Real Number
The set of all rational numbers and irrational numbers. Any number on the number line.
Repeating Decimal
A decimal with a pattern of a fixed number of digits that repeats forever.
Terminating Decimal
A decimal that ends, or terminates.
Theorem
A general mathematical statement that has been proven true.
Converse
A statement that is formed by interchanging the hypothesis and conclusion of the original statement. In other words, the parts of the sentence change places. The words "if" and "then" do not move. (Example statement: "If the sun is out, then it is daytime." CHANGES TO "If it is daytime, then the sun is out.")
Perfect square
A number whose square root is a whole number.
Perfect cube
A number whose cube root is a whole number.
Indirect measurement
A technique that uses proportions to find a measurement when direct measurement is not possible.
Integer
The whole numbers and their opposites (i.e. a number in the set: {...-4, -3, -2, -1, 0, 1, 2, 3, 4...}.
Whole Number
The counting numbers and 0 (i.e. a number in the set: {0, 1, 2, 3, 4...}.
Natural Number
The counting numbers (i.e. a number in the set: {1, 2, 3, 4...}.
Squaring
(a) NUMERIC DEFINITION: Multiplying a number by itself. Example: 5^2 = 25 because 5x5 = 25. (b) GEOMETRIC DEFINITION: A value that represents the area of a square whose side lengths are given.
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