Building Blocks
A fixed and well-defined number or value that does not change, like π or 5.
constant
A triangle with one angle measuring exactly 90 degrees.
right triangle
The complete set of all possible input values for which a function is defined.
domain
A proposition that is believed to be true but has not been formally proven.
conjecture
To rewrite an expression in a simpler or more compact form.
to simplify
A statement of equality between two mathematical expressions, denoted by the symbol =.
equation
A triangle in which all three sides are a different length.
scalene triangle
A relation where each input is related to exactly one output, denoted as f(x).
function
A smaller, helper theorem used as a stepping stone to prove a more significant theorem.
lemma
To break down an expression into a product of simpler expressions, like turning x² - 4 into (x-2)(x+2).
to factor
A symbol, like x or y, that represents a quantity that can change or is unknown.
variable
Two angles whose measures add up to 90 degrees.
complementary angles
A measure of the steepness and direction of a line, representing the rate of change.
slope or gradient
A rigorous and logical argument that establishes the truth of a theorem beyond any doubt.
proof
The smallest number that is a common multiple of the denominators of two or more fractions.
the least common denominator (LCD)
A statement that is accepted as true without proof, serving as a starting point for reasoning.
axiom or postulate
A perpendicular segment from a vertex of a triangle to the line containing the opposite side.
altitude or height
the quantity that influences a function's output but is held constant in a specific scenario, like *m* and *b* in f(x)=mx+b.
parameter
To demonstrate that a statement is false, often by providing a counterexample.
to disprove
To find a number that is close enough to the correct value, often for the purpose of estimation.
to approximate
A numerical or constant multiplier of a variable in an algebraic term, like the 5 in 5x².
coefficient
The angles opposite each other when two lines cross; they are always congruent.
vertical angles
A value that satisfies an equation, making it true; for a function f(x), it's a value *x* such that f(x) = 0.
solution or root
A proposition that follows directly from a proven theorem with little additional proof.
corollary
A fraction where the numerator is greater than or equal to the denominator, like 5/4.
an improper fraction