A–F

AA similarity theorem

Two triangles are similar if they have two corresponding angles that are congruent.

two triangles representing AA similarity theorem
absolute value

A number’s distance from zero on the number line.

The symbol means the absolute value of .

Recall that distance is always positive.

The diagram shows that and .

number line explaining absolute value x–2–2–2–1–1–1111222000
absolute value function

A function that contains an algebraic expression within absolute value symbols. The absolute value parent function, written as:

an absolute value function on a graph x–3–3–3–2–2–2–1–1–1111222333y111222333000
adjacent
angles and triangles with adjacent angles marked 222111BACDABC
adjacent angles

Two non-overlapping angles with a common vertex and one common side.

and are adjacent angles:

adjacent angles commonvertexcommon side12
alternate exterior angles

A pair of angles formed by a transversal intersecting two lines. The angles lie outside of the two lines and are on opposite sides of the transversal.

See angles made by a transversal.

lines crossing creating alternate exterior angles
alternate interior angles

A pair of angles formed by a transversal intersecting two lines. The angles lie between the two lines and are on opposite sides of the transversal.

See also angles made by a transversal.

lines crossing creating alternate interior angles 12transversalbetweenthe lines
altitude

Altitude of a triangle:

A perpendicular segment from a vertex to the line containing the base.

Altitude of a solid:

A perpendicular segment from a vertex to the plane containing the base.

altitude of triangles and cones marked ACDBHMGFEFDEJ
angle

Two rays that share a common endpoint called the vertex of the angle.

lines creating angles
angle bisector

A ray that has its endpoint at the vertex of the angle and divides the angle into two congruent angles.

a line cutting and angle in half
angle of depression/angle of elevation

Angle of depression: the angle formed by a horizontal line and the line of sight of a viewer looking down. Sometimes called the angle of decline.

Angle of elevation: the angle formed by a horizontal line and the line of sight of a viewer looking up. Sometimes called the angle of incline.

angle of elevation ad depression horizontalhorizontalangle ofdepressionangle ofelevation
angles associated with circles: central angle, inscribed angle, circumscribed angle

Central angle: An angle whose vertex is at the center of a circle and whose sides pass through a pair of points on the circle.

central angle in triangle vertexcentralangle

Inscribed angle: An angle formed when two secant lines, or a secant and tangent line, intersect at a point on a circle.

inscribed angle in a circle vertexcenter of circleinscribed angle

Circumscribed angle: The angle made by two intersecting tangent lines to a circle.

circumscribed angle
angles made by a transversal
angles made by transversal corresponding anglessame-side interior anglesAngles made by atransversal andparallel linesalternate exterior anglesalternate interior angles12135416
arc length

The distance along the arc of a circle. Part of the circumference.

Equation for finding arc length:

Where is the radius and is the central angle in radians.

A circle with a segment created from 2 radii
arc of a circle, intercepted arc

Arc: A portion of a circle.

Intercepted arc: The portion of a circle that lies between two lines, rays, or line segments that intersect the circle.

arc of a circle arcinterceptedarc
asymptote

A line that a graph approaches, but does not reach. A graph will never touch a vertical asymptote, but it might cross a horizontal or an oblique (also called slant) asymptote.

Horizontal and oblique asymptotes indicate the general behavior of the ends of a graph in both positive and negative directions. If a rational function has a horizontal asymptote, it will not have an oblique asymptote.

Oblique asymptotes only occur when the numerator of has a degree that is one higher than the degree of the denominator.

a diagram showing vertical asymptotes between curves verticalasymptoteverticalasymptote
a diagram showing the oblique asymptote within a 1/x function obliqueasymptote
a diagram showing the horizontal asymptote within a 1/x function