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1. Geometry Vocabulary
Alphabetical Listing
Acute Angle: An angle with measure between and .
Acute Triangle: A triangle with three acute angles.
Adjacent Angles: Two angles with a common vertex and side but no common interior points.
Alternate Exterior Angles: Two angles that are formed by two lines and a transversal, and lie
outside the two lines on opposite sides of the transversal. are alternate exterior angles
as are .
Alternate Interior Angles: Two angles that are formed by two lines and a transversal, and lie
between the two lines on opposite sides of the transversal. are alternate interior as are
.
Altitude: The perpendicular segment from a vertex to the opposite side or the line containing the
opposite side.

2. Angle: The figure formed by two rays with the same endpoint. The symbol for angle is .
Angle Bisector: A ray that divides an angle into two congruent angles.
Apex: The common point of the lateral faces of a pyramid or cone.
Arc: A connected section of the circumference of a circle.
Area: The amount of surface covered by a plane figure.
Base of a Parallelogram: Either pair of parallel sides of a parallelogram.
Base of a Prism: Either of the congruent parallel polygonal sides.
base
base
bases

3. Base of a Pyramid: The polygonal side of a pyramid that does not contain the apex.
Base of a Trapezoid: Either of the two parallel sides of a trapezoid.
Base of Triangle: The side a triangle that is perpendicular to the altitude.
Bisect: To divide into two congruent parts.
Central Angle: The angle formed by two radii whose vertex lies at the center of a circle.
Centroid: The point at which the three medians of a triangle intersect.
Chord: A segment whose endpoints are points on a circle.

4. Circle: The set of all points in a plane at a given distance, called the radius, from a fixed point on
the plane, called the center.
Circumference: The distance around a circle. Two formulas to find circumference are
and .
Circumscribed: A figure surrounded by a circle intersecting all of the vertices of the figure.
Collinear: Points that lie on the same line.
Complementary Angles: Two angles whose measures have a sum of .
Concave Polygon: A polygon that has an indentation.
Conclusion: The “then” part of an if-then conditional statement.
Conditional Statement: A statement with two parts: a hypothesis or “if” part and a conclusion or
“then” part. Conditional statements are also called if-then statements.
Cone: A geometric solid formed with a circular base and a vertex (apex) that is not in the same
plane as the base.
Congruent: Two figures having the same shape and size. The symbol for congruent is .
Congruent Figures: Two geometric figures that have exactly the same size and shape.
Conjecture: An unproven statement that is based on a pattern or observation.
Construction: A geometric drawing created using only a compass and a straight edge.
Converse: The statement formed by switching the hypothesis and the conclusion of an if-then
statement.
Convex Polygon: A polygon in which no line that contains a side of the polygon passes through
the interior of the polygon.

5. Coordinate: The real number that corresponds to a point on a line
Coplanar Lines: Lines that lie on the same plane.
Coplanar Points: Points that lie on the same plane.
Corollary: A statement that can be easily proven from a theorem.
Corresponding Angles: Two angles that are formed by two lines and a transversal, and occupy
the same relative position. In the diagram are corresponding as are .
Corresponding Parts: The sides and angles in the same relative position between two congruent
figures.
Cosine: A trigonometric ratio, abbreviated as cos, computed as the ratio of the length of the leg
adjacent to the angle to the length of the hypotenuse of the right triangle.
Counterexample: An example that shows that a conjecture is false.
Cross Product: If two ratios are equal, then the product of the numerator with the denominator of
the other ratio is equal to the product of the numerator of the second ratio and the denominator of
the first ratio. If , then ad = bc.
Cylinder: A geometric solid with two congruent circular bases that lie in parallel planes.
Decagon: A polygon with ten sides.

6. Deductive Reasoning: Using facts, definitions, accepted properties, and the laws of logic to
make a logical argument.
Diagonal: A segment that joins two nonconsecutive vertices of a polygon.
Diameter: A chord that passes through the center of a circle. The diameter is twice the radius.
Dilation: A transformation that results in either a reduction or enlargement of the original figure.
Distance: A numeric value that represents how far apart two points are.
Dodecagon: A polygon with 12 sides.
Enlargement: A dilation in which the image is larger than the original figure. The scale factor is
greater than 1.
Equiangular: A polygon having all interior angles congruent.
Equidistant: The same distance.
Equilateral: A polygon with all sides congruent.
Extremes of a Proportion: The first and last terms of a proportion. For the proportions a:b = c:d
and , a and d are the extremes.
Height of a Cone: The shortest distance from the apex to the circular base. The segment is often
called an altitude.

7. Height of a Cylinder: The shortest distance between the two parallel circular bases. The
segment is often called an altitude.
Height of a Parallelogram: The shortest distance between the bases. The segment is often
called an altitude.
Height of a Prism: The shortest distance between the two congruent parallel polygonal bases.
The segment is often called an altitude.
Height of a Pyramid: The shortest distance between the apex to the polygonal base. The
segment is often called an altitude.
Height of a Trapezoid: The shortest distance between two parallel bases. The segment is often
called an altitude.
Height of a Triangle: The shortest distance between a vertex and a line containing the opposite
side. The segment is often called an altitude.
Hemisphere: Half of a sphere.
Heptagon: A polygon having seven sides.
Hexagon: A polygon having six sides.

8. Hypotenuse: In a right triangle, the side opposite the right angle.
If-Then Statement: A statement with two parts: a hypothesis or “if” part and a conclusion or “then”
part. If-then statements are also called conditional statements.
Image: The new figure that results from the transformation of a figure in a plane.
Inductive Reasoning: A process that includes using patterns and observations to make
conjectures.
Inscribed Angle: An angle whose vertex is on a circle and whose sides contain chords of the
circle.
Inscribed Polygon: A polygon whose vertices all lie on a circle that goes around the polygon.
Intersection: The common point(s) shared by two figures.
Isosceles Trapezoid: A trapezoid with congruent legs.
Isosceles Triangle: A triangle with at least two congruent legs.
Lateral Area: The sum of the areas of the lateral faces of a geometric solid.
Lateral Face: A side of a geometric solid that is not a base.
Legs of a Right Triangle: The sides of a right triangle that form the right angle.
Length: The distance between the endpoints of a segment.
Line: A one dimensional object that extends without end in two directions. It is represented by a
line with two arrowheads.

9. Line of Symmetry: A line that forms a reflection of a figure onto itself. It is also called an axis of
symmetry.
Linear Pair: Two adjacent angles whose non-common sides are on the same line.
Major Arc: A connected section of the circumference of a circle that is greater than half of the
circle.
Means of a Proportion: The inner most terms of a proportion. In the proportions a:b = c:d and
, the means are b and c.
Median of a Triangle: A segment from a vertex to the midpoint of the opposite side.
Midpoint: The point on a segment that divides it into to congruent segments.
Mid-segment of a Trapezoid: The segment connecting the midpoints of the legs of a trapezoid.
It is also known as a median.
Mid-segment of a Triangle: The segment connecting the midpoints of the legs of a triangle.
Minor Arc: A connected section of the circumference of a circle that is less than half of the circle.
Nonagon: A polygon having nine sides.
Obtuse Angle: An angle with a measure between .

10. Obtuse Triangle: A triangle with one obtuse angle.
Octagon: A polygon having eight sides.
Parallel Lines: Two lines that lie in the same plane and do not intersect. The symbol for parallel
is ||.
Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
Pentagon: A polygon having five sides.
Perpendicular Bisector: A line that is perpendicular to a segment at its midpoint.
Perpendicular Lines: Two lines that intersect to form a right angle. The symbol for perpendicular
is .
Pi: The ratio of the circumference of a circle to its diameter. Pi is an irrational number denoted by
the symbol .
Plane: A flat two dimensional surface having no thickness and continuing on forever in two
directions. A plane is represented by a shape that looks like a floor or a wall.
Point: A geometric figure having no dimensions. It is represented by a small dot.
Polygon: A plane figure that is formed by three or more segments connected one at each vertex.
Polyhedron: A three-dimensional geometric solid that is formed by polygons. The plural of
polyhedron is polyhedra.
Postulate: A statement that is accepted without further justification.
Principal Square Root: The positive square root.

11. Prism: A polyhedron with two congruent faces, called bases, which lie in parallel planes and the
lateral faces are rectangles.
Proof: A convincing argument that shows why a statement is true.
Proportion: An equation that states two ratios are equal. For example,
Pyramid: A polyhedron in which the base is a polygon and the lateral faces are triangles with a
common vertex called the apex.
Pythagorean Theorem: In a right triangle, the sum of the squares of the legs equals the square
of the hypotenuse.
Quadrilateral: A polygon having four sides.
Radical Expression: A mathematical expression containing or .
Radical Sign: The symbol or used to indicate square roots and nth
roots.
Radicand: The number under the (radical) symbol. It is the number that is having its square
root taken (or 3rd
root or 4th
root or nth
root). In the expression , the radicand is 5.
Radius: A line segment between the center and a point on the circle or sphere. The word radius
also refers to the length of this segment.
Ratio: A comparison between two quantities usually written as a fraction.
Ray: The figure formed by the set of all points beginning from an endpoint continuing on in one
direction forever.
Rectangle: A parallelogram with four right angles.
Reduction: A dilation in which the image is smaller than the original figure.

12. Reflection: A transformation in which a geometric figure is flipped over a line, axis of reflection,
forming a mirror image.
Regular Polygon: A polygon that is both equilateral and equiangular.
Rhombus: A parallelogram with four congruent sides.
Right Angle: An angel with measure .
Right Triangle: A triangle having one right angle.
Rotation: A transformation in which a figure is turned about a fixed point.
Rotational Symmetry: The property of a figure that can be mapped onto itself by turning it less
than .
Same-Side-Interior Angles: Two angles that are formed by two lines and a transversal and lie
between the two lines on the same side of the transversal. In the diagram are same-
side-interior as are .
Scale Factor: The ratio of the lengths of two corresponding sides of two similar polygons.

13. Scalene Triangle: A triangle with no congruent sides.
Secant: A line that intersects a circle in two points.
Sector: A region of a circle determined by two radii and a part of the circle.
Segment: Part of a line that consists of two points, called endpoints, and all points on the line that
are between the endpoints.
Segment Bisector: A segment, ray, line, or plane that intersects a segment at its midpoint.
Semicircle: An arc whose central angle measures . It forms half of a circle.
Similar Polygons: Two polygons in which corresponding angles are congruent and
corresponding side lengths are proportional. The symbol for similar is .
Sine: A trigonometric ratio, abbreviated as sin, computed by the ratio of the length of the leg
opposite the angle to the length of the hypotenuse of the right triangle.
Skew Lines: Two lines that do not lie in the same plane and do not intersect.

14. Slant Height: The shortest diagonal distance from the apex of a cone or pyramid to the base.
Slope: The ratio of the vertical change (rise) to the horizontal change (run) between any two
points on a line.
Solid: A three dimensional figure.
Solve a Right Triangle: Determining the measures of both acute angles and the lengths of all
three sides.
Sphere: A three dimensional solid formed by all the points equidistant from a fixed point, called
the center.
Square: A parallelogram with four right angles and four congruent sides.
Square Root: The number that when multiplied by itself yields a given number. For example, 3 is
the square root of 9 because (3)(3) = 9. The symbol for square root is . A square root is also
called a radical.
Straight Angle: An angle with a measure of .
Supplementary Angles: Two angles whose measures have a sum of .
Tangent: A line in the plane of a circle that intersects the circle in exactly one point called the
point of tangency.
Tangent of an Angle: A trigonometric ratio, abbreviated as tan, that is computed as the ratio of
the length of the leg opposite the angle to the length of the leg adjacent to the angle.

15. Tessellation: A pattern formed by interlocking congruent shapes.
Theorem: A true statement that follows from other true statements. It can also be thought of as a
statement proven to be true.
Transformation: An operation that maps or moves a figure onto an image.
Translation: A transformation that slides each point of a figure the same distance in the same
direction.
Transversal: A line that intersects two or more coplanar lines at different points.
Trapezoid: A quadrilateral with exactly one pair of parallel sides called bases.
Triangle: A polygon having three sides.
Trigonometric Ratio: A ratio of the lengths of two sides of a right triangle.
Undecagon: A polygon having eleven sides.
transversal

16. Vertex: A point that joins two sides of a figure.
Vertical Angles: Two angles that are not adjacent and whose sides are formed by two
intersecting lines. In the diagram are vertical as are .
Volume: The number of cubic units contained within the interior of a solid.