Florida Geometry EOC key terms

A single specific case that shows a general statement is false. If a claim says all quadrilaterals have four equal sides, one rectangle with unequal sides disproves it.

A sentence in if-then form, where the part after "if" is the hypothesis and the part after "then" is the conclusion. It claims the conclusion follows whenever the hypothesis holds.

The statement formed by swapping the hypothesis and conclusion of a conditional. The converse of "if it rains, the ground is wet" is "if the ground is wet, it rained."

The statement formed by negating both the hypothesis and the conclusion of a conditional. Its truth is not automatically the same as the original statement's truth.

The statement formed by swapping and negating both parts of a conditional. It always has the same truth value as the original conditional statement.

A conclusion or pattern rule proposed from limited observations that has not been proven. It may later be supported by a proof or rejected by a counterexample.

Reasoning that uses observed patterns or specific examples to form a general conclusion. Its results are probable but not guaranteed, so they need proof or testing.

Reasoning that moves from accepted statements such as definitions, postulates, and proven theorems to a logically certain conclusion. Valid steps guarantee the conclusion if the premises are true.

A statement about geometry that has been proven true using definitions, postulates, and previously proven results. Once proven, it can be used in later proofs.

A basic statement accepted as true without proof, used as a starting point for reasoning. Examples include the idea that exactly one line passes through two distinct points.

A logical argument that uses definitions, postulates, and proven theorems to show a statement must be true. Each step follows from earlier steps by valid reasoning.

Figures that have exactly the same size and shape, so corresponding sides and corresponding angles are equal in measure. One can be moved onto the other by rigid motions.

A transformation that preserves distance and angle measure, such as a translation, rotation, or reflection. It produces a figure congruent to the original.

Figures with the same shape but not necessarily the same size. Corresponding angles are equal and corresponding side lengths share a constant ratio.

The ratio that compares a length in an image to the matching length in the original figure. It tells how much a figure is enlarged or reduced.

A transformation that stretches or shrinks a figure by a scale factor from a fixed center point. It preserves angle measures and produces a similar figure.

A rigid motion that slides every point of a figure the same distance in the same direction. Side lengths, angles, and orientation stay unchanged.

A rigid motion that flips a figure across a line, called the line of reflection, so each point maps to a mirror-image location. It reverses orientation.

A rigid motion that turns a figure about a fixed center point through a given angle. Distances from the center and angle measures are preserved.

A number describing a line's steepness, found as the change in y divided by the change in x between two points. Parallel lines share it; perpendicular lines have negative reciprocal slopes.

The point that divides a segment into two equal parts. Its coordinates are the averages of the endpoints' x-coordinates and y-coordinates.

A rule giving the length of a segment from its endpoints' coordinates using the square root of the sum of squared differences. It comes from the Pythagorean theorem.

Lines in the same plane that never intersect. When a transversal cuts them, corresponding angles are equal and alternate interior angles are equal.

Lines that intersect to form right angles. Their slopes multiply to negative one when neither line is vertical.

A line that intersects two or more other lines at different points. It creates angle pairs such as alternate interior and corresponding angles used in parallel-line reasoning.

A pair of angles on opposite sides of a transversal and between the two lines it crosses. They are equal in measure when those lines are parallel.

The rule that in a right triangle the square of the hypotenuse equals the sum of the squares of the legs. Written as a squared plus b squared equals c squared.

The side of a right triangle opposite the right angle. It is always the longest side and is the side labeled c in the Pythagorean theorem.

A ratio comparing two sides of a right triangle, such as sine, cosine, or tangent. These ratios depend on an acute angle and are used to find unknown sides or angles.

For an acute angle in a right triangle, the ratio of the length of the opposite leg to the length of the hypotenuse. It helps find missing parts of right triangles.

For an acute angle in a right triangle, the ratio of the length of the adjacent leg to the length of the hypotenuse. It pairs with sine in right-triangle problems.

An angle whose vertex is the center of a circle and whose sides are radii. Its measure equals the measure of the arc it intercepts.

An angle whose vertex lies on a circle and whose sides are chords. Its measure is half the measure of its intercepted arc.

A portion of a circle between two points on it. It is measured in degrees by its central angle and in length as a fraction of the circumference.

The distance around a circle, calculated as pi times the diameter, or two times pi times the radius. It is the circle's perimeter.

The amount of flat space enclosed by a circle, found by multiplying pi by the square of the radius. It is measured in square units.

A region of a circle bounded by two radii and the arc between them, shaped like a slice of pie. Its area is a fraction of the circle's area based on the central angle.

The amount of space a three-dimensional solid occupies, measured in cubic units. Common formulas use base area times height for prisms and cylinders.

The total area of all the faces or curved surfaces of a three-dimensional solid, measured in square units. It represents the material needed to cover the solid.

The probability that an event occurs given that another event has already occurred. It is computed as the probability of both events divided by the probability of the given event.

A table that displays counts of two categorical variables, showing totals for rows and columns. It is used to find joint, marginal, and conditional probabilities.