Glossary of Terms for a Geometry Course
45-45-90 triangle
A special type of right triangle where the two legs are congruent, and the angles measure 45°, 45°, and 90°.
30-60-90 triangle
A special type of right triangle with angles measuring 30°, 60°, and 90°, and the sides in the ratio 1:√3:2.
AA similarity
A rule stating that two triangles are similar if two corresponding angles are congruent.
Acute angle
An angle that measures less than 90°.
Acute triangle
A triangle where all three angles are acute (less than 90°).
Adjacent angles
Two angles that share a common side and a common vertex.
Alt int angles
Angles located on opposite sides of a transversal and inside the two lines it intersects.
Alt ext angles
Angles located on opposite sides of a transversal and outside the two lines it intersects.
Angle
A figure formed by two rays sharing a common endpoint called the vertex.
Angle bisector
A ray that divides an angle into two congruent angles.
Arc
A continuous portion of a circle.
Arc length
The distance along a circular arc, calculated as a portion of the circumference.
ASA congruence
A rule stating that two triangles are congruent if two angles and the included side are equal.
AAS congruence
A rule stating that two triangles are congruent if two angles and a non-included side are equal.
Biconditional
A logical statement where both the original statement and its converse are true.
Bisector
A line, segment, or ray that divides a figure into two congruent parts.
Central angle
An angle whose vertex is at the center of a circle and whose sides are radii.
Chord
A segment whose endpoints lie on a circle.
Collinear points
Points that lie on the same straight line.
Compass and straightedge
Tools used in classical geometry for constructing figures and performing geometric tasks.
Complementary angles
Two angles whose measures add up to 90°.
Composite transformations
A combination of two or more geometric transformations.
Conditional statement
A logical statement that has two parts: a hypothesis and a conclusion, often written in "if-then" form.
Congruent figures
Figures that have the same size and shape.
Congruent triangles
Triangles that are identical in size and shape, with corresponding sides and angles equal.
Converse
The statement formed by reversing the hypothesis and conclusion of a conditional statement.
Coplanar points
Points that lie on the same plane.
Cross section
A two-dimensional shape obtained by slicing a three-dimensional figure.
Cylinder
A three-dimensional figure with two congruent circular bases connected by a curved surface.
Deductive reasoning
A logical process in which a conclusion follows necessarily from the given premises.
Diameter
A chord that passes through the center of a circle.
Dilation
A transformation that changes the size of a figure but preserves its shape.
Distance formula
A formula used to calculate the distance between two points in a plane.
Directed line segment
A segment with a specific direction, defined by an initial point and a terminal point.
Euler's formula
A formula relating the vertices (V), edges (E), and faces (F) of a polyhedron: \( V - E + F = 2 \).
Equation of circle
The formula \( (x-h)^2 + (y-k)^2 = r^2 \), representing a circle with center \((h, k)\) and radius \(r\).
Exterior angle theorem
A theorem stating that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
Flowchart proof
A proof presented as a diagram showing a logical sequence of steps with arrows connecting them.
Glide reflection
A transformation combining a reflection and a translation along the line of reflection.
Image
The result of applying a transformation to a figure.
Inductive reasoning
A logical process of forming a generalization based on specific observations or examples.
Isometry
A transformation that preserves distances, resulting in congruent figures.
Kite
A quadrilateral with two pairs of adjacent sides congruent and one pair of opposite angles congruent.
Linear pair
A pair of adjacent angles whose non-common sides form a straight line.
Line symmetry
A property where a figure can be divided into two mirror-image halves by a line.
Midpoint
The point that divides a segment into two equal parts.
Parallel lines
Two lines in the same plane that never intersect.
Perpendicular bisector
A line, segment, or ray that is perpendicular to a segment at its midpoint.
Perpendicular lines
Two lines that intersect to form a right angle.
Point
A location in space with no size or dimension.
Polygon interior angles
The angles inside a polygon, with the sum determined by \((n-2) \times 180^\circ\), where \(n\) is the number of sides.
Proportional sides
Corresponding sides of similar figures that have the same ratio.
Pythagorean theorem
A theorem stating that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Radius
A segment from the center of a circle to any point on the circle.
Ray
A part of a line that starts at a point and extends infinitely in one direction.
Reflex angle
An angle that measures more than 180° but less than 360°.
Right angle
An angle that measures exactly 90°.
Rotational symmetry
A property of a figure that can be rotated about a point by a certain angle and still look the same.
Scalene triangle
A triangle with no congruent sides.
Slope
A measure of the steepness of a line, calculated as the ratio of the vertical change to the horizontal change.
SSS congruence
A rule stating that two triangles are congruent if all three pairs of corresponding sides are equal.
SSS similarity
A rule stating that two triangles are similar if their corresponding sides are proportional.
Tangent
A line that touches a circle at exactly one point.
Tessellation
A pattern of shapes that fit together without gaps or overlaps.
Transformation
A change in the position, size, or shape of a figure.
Transversal
A line that intersects two or more lines at distinct points.
Triangle inequality
A rule stating that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Vertex
The common endpoint of two rays or segments in an angle, polygon, or polyhedron.
Vertical angles
Two angles formed by intersecting lines, sharing a common vertex but not a common side.