Florida Geometry EOC flashcards
Florida Geometry EOC · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Contrapositive
- The statement formed by negating and swapping a conditional's hypothesis and conclusion. It is always logically equivalent to the original conditional statement.
- Law of Detachment
- A reasoning rule stating that if a conditional p implies q is true and p is true, then q must be true.
- Counterexample
- A single specific case in which a statement's hypothesis is true but its conclusion is false, proving the statement is not universally valid.
- Vertical angles
- Two nonadjacent angles formed by intersecting lines. They are always congruent and share only a vertex, not a side.
- Biconditional statement
- A statement of the form p if and only if q, true exactly when both the conditional and its converse are true.
- SSS congruence
- A triangle congruence criterion: if three sides of one triangle are congruent to three sides of another, the triangles are congruent.
- AA similarity
- A triangle similarity criterion: if two angles of one triangle are congruent to two angles of another, the triangles are similar.
- Scale factor
- The ratio k comparing corresponding lengths of two similar figures; areas compare as k squared and volumes as k cubed.
- CPCTC
- An abbreviation meaning corresponding parts of congruent triangles are congruent, used after congruence of the whole triangles is established.
- Triangle midsegment
- A segment joining the midpoints of two sides of a triangle; it is parallel to the third side and half its length.
- Distance formula
- The formula giving the distance between two points: the square root of the sum of the squared differences of their x- and y-coordinates.
- Perpendicular slope relationship
- Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product of the slopes equals negative one.
- Rotation 90 degrees counterclockwise
- A transformation about the origin mapping each point (x, y) to the point with coordinates (negative y, x).
- Dilation
- A transformation that multiplies all distances from a fixed center by a scale factor, producing a similar figure without changing angle measures.
- Midpoint formula
- The coordinates of a segment's midpoint are the averages of the endpoints' x-coordinates and of their y-coordinates.
- Pythagorean Theorem
- In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs; its converse identifies right triangles.
- Sine ratio
- In a right triangle, the sine of an acute angle equals the length of the side opposite that angle divided by the hypotenuse length.
- 30-60-90 triangle
- A right triangle whose acute angles measure 30 and 60 degrees; its sides are in the ratio one to square root of three to two.
- Law of Cosines
- A relationship stating the square of a side equals the sum of the squares of the other two sides minus twice their product times the cosine of the included angle.
- Angle of elevation
- The angle measured upward from a horizontal line to a line of sight directed at an object above the observer.
- Inscribed angle
- An angle whose vertex lies on a circle and whose sides are chords; its measure is half the measure of its intercepted arc.
- Tangent-radius theorem
- A line tangent to a circle is perpendicular to the radius drawn to the point where the line touches the circle.
- Chord-chord product
- When two chords intersect inside a circle, the products of the two segment lengths on each chord are equal.
- Arc length formula
- The length of an arc equals the central angle divided by 360 degrees, multiplied by the circle's circumference.
- Circle equation
- The standard form (x minus h) squared plus (y minus k) squared equals r squared describes a circle with center (h, k) and radius r.
- Cone volume
- The volume of a cone equals one third of pi times the radius squared times the height, one third of the matching cylinder's volume.
- Sphere surface area
- The total area covering a sphere, computed as four times pi times the radius squared.
- Composite figure area
- The area of an irregular region found by splitting it into standard shapes and adding, or by subtracting removed shapes from a larger one.
- Similar solids scaling
- When all dimensions of a solid are multiplied by k, surface area is multiplied by k squared and volume by k cubed.
- Geometric probability
- The probability a randomly chosen point lies in a region, computed as the favorable length, area, or volume divided by the total.
- Complement rule
- The probability that an event does not occur equals one minus the probability that the event does occur.
- Expected value
- The long-run average of a random quantity, computed by summing each possible value multiplied by its probability.