Geometry Important Vocabulary

This set of vocabulary flashcards provides a comprehensive review of fundamental terms, properties, and theorems for high school geometry, covering basic components, shapes, circles, transformations, and right triangle trigonometry.

Point

An exact location in space. It has no length, width, or thickness.

Line

A straight path that extends infinitely in both directions.

Plane

A flat surface that extends infinitely in all directions.

Collinear

Points that lie on the same line.

Coplanar

Points or figures that lie in the same plane.

Segment

A part of a line with two endpoints.

Ray

A part of a line with one endpoint that extends infinitely in one direction.

Opposite Rays

Two rays that share an endpoint and form a straight line.

Endpoint

A point at the end of a segment or the starting point of a ray.

Midpoint

The point that divides a segment into two congruent segments.

Congruent

Having the same size and shape; corresponding measures are equal.

Angle

A figure formed by two rays with a common endpoint.

Vertex

The common endpoint of two rays that form an angle.

Adjacent Angles

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

Complementary Angles

Two angles whose measures add to $90^{\circ}$.

Supplementary Angles

Two angles whose measures add to $180^{\circ}$.

Vertical Angles

Opposite angles formed when two lines intersect. They are congruent.

Linear Pair

Two adjacent angles whose noncommon sides form a straight line.

Perpendicular Lines

Lines that intersect to form right angles.

Parallel Lines

Coplanar lines that never intersect and remain the same distance apart.

Transversal

A line that intersects two or more coplanar lines.

Corresponding Angles

Angles in the same relative position when a transversal crosses two lines.

Alternate Interior Angles

Interior angles on opposite sides of a transversal.

Alternate Exterior Angles

Exterior angles on opposite sides of a transversal.

Same-Side Interior Angles

Interior angles on the same side of a transversal; with parallel lines, they are supplementary.

Polygon

A closed plane figure made of three or more line segments.

Triangle

A polygon with three sides and three angles.

Equilateral Triangle

A triangle with three congruent sides.

Isosceles Triangle

A triangle with at least two congruent sides.

Scalene Triangle

A triangle with no congruent sides.

Right Triangle

A triangle containing one $90^{\circ}$ angle.

Acute Triangle

A triangle in which all three angles are less than $90^{\circ}$.

Obtuse Triangle

A triangle containing one angle greater than $90^{\circ}$.

Triangle Inequality Theorem

The sum of any two side lengths of a triangle must be greater than the third side length.

Quadrilateral

A polygon with four sides and four angles.

Parallelogram

A quadrilateral with both pairs of opposite sides parallel.

Rectangle

A parallelogram with four right angles.

Rhombus

A parallelogram with four congruent sides.

Square

A quadrilateral with four congruent sides and four right angles.

Trapezoid

A quadrilateral with at least one pair of parallel sides.

Kite

A quadrilateral with two distinct pairs of consecutive congruent sides.

Similarity

A relationship between figures with the same shape but not necessarily the same size.

Similar Figures

Figures whose corresponding angles are congruent and corresponding sides are proportional.

Scale Factor

The ratio used to compare corresponding lengths of similar figures.

Proof

A logical argument that uses definitions, postulates, theorems, and known facts to show a statement is true.

Theorem

A mathematical statement that has been proven true.

Postulate

A statement accepted as true without proof.

Conjecture

A statement believed to be true based on observations but not yet proven.

Conditional Statement

A statement written in 'if-then' form.

Hypothesis

The 'if' part of a conditional statement.

Conclusion

The 'then' part of a conditional statement.

Transformation

A change in the position, size, or orientation of a figure.

Translation

A transformation that slides a figure without turning or flipping it.

Reflection

A transformation that flips a figure across a line of reflection.

Rotation

A transformation that turns a figure around a fixed point.

Dilation

A transformation that changes the size of a figure using a scale factor.

Rigid Transformation

A transformation that preserves lengths and angle measures.

Coordinate Plane

A plane formed by a horizontal x-axis and vertical y-axis.

Distance Formula

A formula used to find the distance between two points in a coordinate plane.

Midpoint Formula

A formula used to find the point halfway between two points.

Slope

The rate of change of a line; rise divided by run.

Area

The amount of space inside a two-dimensional figure.

Perimeter

The total distance around a two-dimensional figure.

Circumference

The distance around a circle.

Radius

A segment from the center of a circle to a point on the circle.

Diameter

A segment passing through the center of a circle with endpoints on the circle.

Chord

A segment with both endpoints on a circle.

Tangent

A line that intersects a circle at exactly one point.

Secant

A line that intersects a circle at two points.

Arc

A portion of a circle.

Central Angle

An angle whose vertex is at the center of a circle.

Inscribed Angle

An angle whose vertex is on a circle and whose sides are chords.

Pythagorean Theorem

In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse: $a^2 + b^2 = c^2$.

Hypotenuse

The side opposite the right angle in a right triangle; it is the longest side.

Legs

The two sides that form the right angle in a right triangle.

Trigonometric Ratios

Ratios relating the sides of a right triangle to one of its acute angles: sine, cosine, and tangent.