Geometry Terms and Concepts from Common Core 2019

Line

A straight one-dimensional figure having no thickness and extending infinitely in both directions.

Plane

A flat two-dimensional surface that extends infinitely in all directions.

Collinear Points

Points that lie on the same straight line.

Coplanar Points

Points that lie in the same plane.

Segment

A part of a line that is bounded by two distinct end points.

Ray

A part of a line that starts at one point and extends infinitely in one direction.

Opposite Rays

Two rays that share the same endpoint and extend in opposite directions.

Intersection

The point or set of points where two or more geometric figures meet.

Ruler Postulate

The distance between any two points on a line can be measured using a ruler.

Coordinate

A set of values that show an exact position.

Distance

The length of the shortest path between two points.

Construction

A method of creating geometric figures using a compass and straightedge.

Segment Addition Postulate

If point B is between points A and C, then AB + BC = AC.

Midpoint

The point that divides a segment into two equal parts.

Segment Bisector

A line, ray, or segment that intersects a segment at its midpoint.

Midpoint Formula

The formula to find the midpoint M of a segment with endpoints (x1, y1) and (x2, y2): M = ((x1 + x2)/2, (y1 + y2)/2).

Distance Formula

The formula to find the distance d between two points (x1, y1) and (x2, y2): d = √((x2 - x1)² + (y2 - y1)²).

Polygon classification

The categorization of polygons based on the number of sides and angles.

Angle

The figure formed by two rays with a common endpoint.

Vertex

The common endpoint of the rays that form an angle.

Interior of an angle

The region inside the angle.

Exterior of an angle

The region outside the angle.

Measure

The size of an angle in degrees.

Acute Angle

An angle that measures less than 90 degrees.

Right Angle

An angle that measures exactly 90 degrees.

Obtuse Angle

An angle that measures more than 90 degrees but less than 180 degrees.

Straight Angle

An angle that measures exactly 180 degrees.

Angle Addition Postulate

If point B is in the interior of angle AOC, then m∠AOB + m∠BOC = m∠AOC.

Complementary Angles

Two angles whose measures add up to 90 degrees.

Supplementary Angles

Two angles whose measures add up to 180 degrees.

Adjacent Angles

Two angles that share a common vertex and side but do not overlap.

Linear Pairs

A pair of adjacent angles that are formed when two lines intersect.

Vertical Angles

The angles opposite each other when two lines intersect.

Conditional Statement

A statement that can be written in the form 'If p, then q.'

If-Then Form

The structure of a conditional statement.

Hypothesis

The part of a conditional statement that follows 'if.'

Conclusion

The part of a conditional statement that follows 'then.'

Negation

The opposite of a given statement.

Converse

The statement formed by reversing the hypothesis and conclusion of a conditional statement.

Inverse

The statement formed by negating both the hypothesis and conclusion of a conditional statement.

Contrapositive

The statement formed by negating and reversing the hypothesis and conclusion of a conditional statement.

Equivalent Statements

Statements that have the same truth value.

Perpendicular Lines

Lines that intersect to form right angles.

Biconditional Statement

A statement that can be written in the form 'p if and only if q.'

Truth Value

The attribute of a statement that determines whether it is true or false.

Truth Table

A table used to determine the truth value of a logical expression.

Conjecture

An educated guess based on observations.

Inductive Reasoning

Reasoning that involves making generalizations based on specific examples.

Counterexample

An example that disproves a conjecture.

Deductive Reasoning

Reasoning that uses facts, definitions, and accepted properties to form a logical conclusion.

Point, Line, Plane Postulates

Basic assumptions about points, lines, and planes that are accepted without proof.

Properties of Equality

Rules that govern the equality of expressions.

Distribution Property

A property that states a(b + c) = ab + ac.

Reflexive Property

For any real number a, a = a.

Symmetric Property

For any real numbers a and b, if a = b, then b = a.

Transitive Property

For any real numbers a, b, and c, if a = b and b = c, then a = c.

Proof

A logical argument that shows a statement is true.

Congruent Supplements Theorem

If two angles are supplements of the same angle, then they are congruent.

Congruent Complements Theorem

If two angles are complements of the same angle, then they are congruent.

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary.

Vertical Angle Theorem

Vertical angles are congruent.

Parallel Lines

Lines in the same plane that never intersect.

Parallel Planes

Planes that do not intersect.

Skew Lines

Lines that do not intersect and are not parallel.

Transversal

A line that intersects two or more lines at different points.

Corresponding Angles

Angles that are in the same position on two parallel lines cut by a transversal.

Alternate Interior Angles

Angles that are on opposite sides of the transversal and inside the two lines.

Consecutive Interior Angles

Angles that are on the same side of the transversal and inside the two lines.

Corresponding Angles Theorem

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary.

Vector

A quantity that has both magnitude and direction.

Initial Point

The starting point of a vector.

Terminal Point

The endpoint of a vector.

Horizontal Component

The horizontal part of a vector.

Vertical Component

The vertical part of a vector.

Component Form

A way to express a vector in terms of its horizontal and vertical components.

Transformation

A function that maps a set of points to another set of points.

Image

The result of a transformation.

Preimage

The original figure before a transformation.

Rigid Motion

A transformation that preserves distance and angle measures.

Composition of Transformations

The combination of two or more transformations.

Reflection

A transformation that flips a figure over a line.

Line of Reflection

The line over which a figure is reflected.

Rotation

A transformation that turns a figure around a fixed point.

Angle of Rotation

The degree measure of the angle through which a figure is rotated.

Point of Rotation

The fixed point around which a figure is rotated.

Rotational Symmetry

A property of a figure that looks the same after a rotation.

Center of Symmetry

The point around which a figure has rotational symmetry.

Congruent Figures

Figures that have the same size and shape.

Congruence Transformation

A transformation that produces a congruent figure.

Dilation

A transformation that changes the size of a figure but not its shape.

Center of Dilation

The point from which a figure is dilated.

Scale Factor

The ratio of the size of the image to the size of the preimage in a dilation.

Similarity Transformation

A transformation that produces a similar figure.

Similar Figures

Figures that have the same shape but not necessarily the same size.

Classifying Triangles by Sides and Angles

The process of categorizing triangles based on their side lengths and angle measures.

Triangle Sum Theorem

The sum of the angles in a triangle is always 180 degrees.

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Triangle Sum Theorem Corollary

The corollary that states that the sum of the measures of the angles in a triangle is 180 degrees.