Ohio OST Geometry key terms

An exact location in space that has no size, length, width, or depth. It is usually named with a capital letter and serves as the building block for all other geometric figures.

A straight one-dimensional figure extending without end in both directions. It has no thickness and is determined completely by any two distinct points lying on it.

The portion of a line bounded by two endpoints, including both endpoints. Its length is the straight-line distance between those two points.

A part of a line that begins at one endpoint and extends without end in one direction. Naming it requires the endpoint first, then another point on the ray.

A flat two-dimensional surface that extends infinitely in all directions. Three noncollinear points determine exactly one plane, and lines and figures can lie within it.

A figure formed by two rays sharing a common endpoint called the vertex. Its measure describes the amount of rotation between the rays, usually in degrees.

The common endpoint where two rays or segments of an angle meet, or the point where two sides of a polygon intersect. In a parabola it is the highest or lowest point.

A ray, segment, or line that passes through the vertex of an angle and divides it into two angles of equal measure. Every point on it is equidistant from the angle's sides.

A line, segment, or ray that intersects a segment at its midpoint and forms right angles with it. Every point on it is equidistant from the segment's two endpoints.

The point that divides a segment into two congruent parts. Its coordinates are the averages of the endpoints' corresponding coordinates in the coordinate plane.

Two or more coplanar lines that never intersect, no matter how far they are extended. They have the same slope in the coordinate plane and stay a constant distance apart.

Two lines that intersect to form four right angles. In the coordinate plane their slopes are negative reciprocals, and their product is negative one.

A line that intersects two or more other lines at distinct points. When it crosses parallel lines, it creates congruent alternate interior, alternate exterior, and corresponding angle pairs.

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

A pair of angles in matching positions at two different intersections made by a transversal. When the intersected lines are parallel, corresponding angles are congruent.

A polygon with exactly three sides and three interior angles. Its interior angle measures always sum to 180 degrees, and its side lengths satisfy the triangle inequality.

An angle formed by one side of a polygon and the extension of an adjacent side. For a triangle, its measure equals the sum of the two remote interior angles.

A closed plane figure made of three or more line segments that meet only at their endpoints. The segments are sides, and the interior angles of an n-gon sum to (n − 2)·180 degrees.

A polygon with all sides congruent and all interior angles congruent. It can be inscribed in a circle, and its center coincides with the center of that circle.

Two triangles whose corresponding sides and corresponding angles are all equal in measure. Standard tests for congruence include SSS, SAS, ASA, AAS, and HL for right triangles.

Figures with the same shape but not necessarily the same size. Corresponding angles are congruent, corresponding side lengths are proportional, and areas compare as the square of the scale factor.

The ratio of a length in a scaled image to the corresponding length in the original figure. It also equals the ratio of any pair of corresponding sides in similar figures.

A transformation that enlarges or reduces a figure by a scale factor from a fixed center point. It preserves angle measures and shape but generally changes side lengths and area.

A transformation that preserves distance and angle measure, such as a translation, rotation, or reflection. Figures related by rigid motions are congruent.

A transformation that slides every point of a figure the same distance in the same direction. It is a rigid motion, so the image remains congruent to the original.

A transformation that flips a figure across a line, producing a mirror image. Each point and its image are the same distance from the line of reflection, which is the perpendicular bisector of the segment joining them.

A transformation that turns a figure about a fixed center point by a given angle measure. It is a rigid motion preserving distance and angle measure.

The relationship stating that in a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. It is used to find unknown side lengths and distances.

The side of a right triangle opposite the right angle. It is always the longest side and is the side squared alone on one side of the Pythagorean equation.

A triangle containing exactly one angle measuring 90 degrees. Its legs and hypotenuse satisfy the Pythagorean theorem, and its acute angles are complementary.

A ratio comparing two side lengths of a right triangle, such as sine, cosine, or tangent. Each ratio depends only on the measure of the acute angle chosen.

The angle measured upward from a horizontal line to a line of sight toward an object above. It is often used with trigonometric ratios to find heights and distances.

The angle measured downward from a horizontal line to a line of sight toward an object below. It is congruent to the angle of elevation measured from the object.

A rule giving the straight-line distance between two points in the coordinate plane. It is derived from the Pythagorean theorem applied to horizontal and vertical differences.

The set of all points in a plane at a fixed distance from a given center point. The fixed distance is the radius, and the figure encloses a region whose area is πr².

A segment from the center of a circle to any point on the circle, or the length of that segment. Every radius of a given circle has the same length.

A chord that passes through the center of a circle, or its length. It equals twice the radius and is the longest chord of the circle.

A segment whose endpoints both lie on a circle. A chord is not necessarily a diameter, but every diameter is a chord.

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

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.

A portion of a circle consisting of two endpoints and the continuous curve between them. Arc measure is given in degrees, while arc length is a distance along the curve.

The point where the three perpendicular bisectors of a triangle's sides meet. It is the center of the circle passing through all three vertices.

A circle drawn inside a polygon so that it touches each side at exactly one point. Its center is the incenter, found where the angle bisectors meet.

The amount of three-dimensional space a solid occupies, measured in cubic units. Formulas differ by solid, such as length × width × height for a rectangular prism.

The total area of all the faces or surfaces of a three-dimensional solid, measured in square units. For a rectangular prism it is 2lw + 2lh + 2wh.

The two-dimensional figure produced when a plane slices through a three-dimensional solid. Its shape depends on both the solid and the orientation of the cutting plane.

A two-dimensional pattern that can be folded to form a three-dimensional solid. The area of the net equals the surface area of the solid it creates.

A statement in if-then form, written p → q, where p is the hypothesis and q is the conclusion. Its truth depends on whether the conclusion must follow from the hypothesis.

The statement formed by swapping the hypothesis and conclusion of a conditional, written q → p. A converse is not automatically true when the original statement is true.

A single case that satisfies the hypothesis of a statement but makes the conclusion false. Finding one proves that a general statement is not true.