A–F

AA similarity theorem

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

two triangles representing AA similarity theorem
acute angle

An angle whose measure is between and .

is an acute angle.

an acute angle
acute triangle

A triangle with three acute angles.

Angles , , and are all acute angles.

Triangle is an acute triangle.

an acute triangle
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
Ambiguous Case of the Law of Sines

The Ambiguous Case of the Law of Sines occurs when we are given SSA information about the triangle. Because SSA does not guarantee triangle congruence, there are two possible triangles.

To avoid missing a possible solution for an oblique triangle under these conditions, use the Law of Cosines first to solve for the missing side. Using the quadratic formula to solve for the missing side will make both solutions become apparent.

ambiguous case of the law of sines
ambiguous case of the law of sines
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
angle of rotation

The fixed point a figure is rotated about is called the center of rotation. If one connects a point in the pre-image, the center of rotation, and the corresponding point in the image, they can see the angle of rotation. A counterclockwise rotation is a rotation in a positive direction. Clockwise is a negative rotation.

angle of rotation positive rotationD is the center of rotationnegative rotation
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