Arccosine is a relationship used to find an acute angle measure in a right triangle when two side lengths are known.

The arccosine of a number between 0 and 1 is the measure of an acute angle whose cosine is that number.

Arcsine is a relationship used to find an acute angle measure in a right triangle when two side lengths are known.

The arcsine of a number between 0 and 1 is the measure of an acute angle whose sine is that number.

Arctangent is a relationship used to find an acute angle measure in a right triangle when two side lengths are known.

The arctangent of a positive number is the measure of an acute angle whose tangent is that number.

An assertion is a statement that someone thinks is true but has not yet proved.

An auxiliary line is an extra line drawn on a figure to show hidden structure.

• The auxiliary line drawn on this isosceles triangle shows a line of symmetry. 
• The auxiliary lines drawn on this parallelogram suggest a way of rearranging it into a rectangle.

Cavalieri’s Principle states that if two solids of equal height are cut into cross-sections by parallel planes, and the corresponding cross-sections on each plane always have equal areas, then the two solids have the same volume.

A chance experiment is something that can be done over and over again, and what will happen each time is not known.

For example, each time the spinner is spun, it could land on red, yellow, blue, or green.

The circumcenter of a triangle is the intersection point of all three perpendicular bisectors of the triangle’s sides. It is the center of the triangle’s circumscribed circle.

In this diagram, the circumcenter is point .

Two angles are complementary to each other if their measures add up to . The two acute angles in a right triangle are complementary to each other.

Conditional probability is the likelihood that one event occurs given that another event occurs.

A conjecture is a reasonable guess that someone is trying to either prove or disprove.

The converse of an if-then statement is the statement that switches the hypothesis and the conclusion.

Example:

• Statement: “If it is raining, then the game is canceled.”
• Converse: “If the game is canceled, then it is raining.”

A cross-section is the two-dimensional figure formed by intersecting a solid with a plane.

These diagrams show that the shape of the cross-section depends on how the plane intersects the solid.

The cube root of a number , written , is the number whose cube is .

That is, . So, .

Example: . So, .

Density is a measure of how tightly the amount of matter in a substance is packed into the space it takes up. That is, density is the mass of a substance per unit volume.

Events are called dependent when they are from the same experiment and where the outcome of one event affects the probability of another.

An event is a set of 1 or more outcomes in a chance experiment.

For example, if a number cube is rolled, there are 6 possible outcomes.

Some events are “rolling a number less than 3,” “rolling an even number,” or “rolling a 5.”

Any flat surface on a three-dimensional figure is a face.

• A cube has 6 faces that are all squares.
• A cylinder has 2 faces that are both circles.

The incenter of a triangle is the intersection point of all three of the triangle’s angle bisectors. It is the center of the triangle’s inscribed circle.

In this diagram the incenter is point .

Events are called independent when they are from the same experiment and the outcome of one event does not affect the probability of another.

When a figure is inscribed, it is completely inside another figure so that their sides, edges, vertices, or curves touch.

• A polygon is inscribed in a circle if it fits inside the circle and every vertex of the polygon is on the circle.
• A circle is inscribed in a polygon if it fits inside the polygon and every side of the polygon is tangent to the circle.

A line of symmetry is a line that divides a figure into two parts that are mirror images of each other. When a figure is reflected across one of its lines of symmetry, it takes the figure onto itself.

These dashed lines show two lines of symmetry for a regular hexagon, and two lines of symmetry for the capital letter I.

An oblique solid is not exactly upright—it seems to lean over at an angle.

• Prisms and cylinders are said to be oblique if the directed line segment that defines the translation between the bases is not perpendicular to the bases.
• A cone is said to be oblique if a line drawn from its apex at a right angle to the plane of its base does not intersect the center of the base. The same definition applies to pyramids whose bases are figures with a center point, such as a square or a regular pentagon.

Two numbers are opposites if they are the same distance from 0 on the number line, but on opposite sides. One is negative, and the other is positive.

An outcome of a chance experiment is one of the things that can happen.

For example, the possible outcomes of tossing a coin are heads and tails.

A prism is a three-dimensional figure composed of two parallel, congruent faces (called bases) connected by parallelograms. A prism is named for the shape of its bases. For example, if a prism’s bases are pentagons, it is called a pentagonal prism.

The probability of a chance event is a number from 0 to 1 that expresses the likelihood of the event occurring, with 0 meaning it will never occur and 1 meaning it will always occur.

A pyramid is a three-dimensional figure that has one special face called the base. All of the other faces are triangles that meet at a single vertex called the apex. A pyramid is named for the shape of its base. For example, if a pyramid’s base is a hexagon, it is called a hexagonal pyramid.

A radian is a unit of measurement for angles, based on the radius of a circle.

The radian measure of any central angle is this ratio:

Two numbers that multiply to equal 1 are reciprocals. 

If is a rational number that is not 0, then the reciprocal of is the number .

A right solid is exactly upright—it does not seem to lean over at an angle.

• Prisms or cylinders are said to be right if the directed line segment that defines the translation between the bases is perpendicular to the bases.
• A cone is said to be right if a line drawn from its apex at a right angle to the plane of its base passes through the center of the base. The same definition applies to pyramids whose bases are figures with a center point, such as a square or a regular pentagon.

A rotation is a rigid transformation that is defined by a center, an angle, and a direction. It takes one point on a circle to another point, using a given center. The two radii—the one from the center to the original point and the one from the center to the image—make the angle of rotation.

In this figure, is the image of after a counterclockwise rotation of using the point as the center.

In this figure, quadrilateral is rotated counterclockwise using the point as the center.

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The sample space is the list of every possible outcome for a chance experiment.

For example, the sample space for tossing two coins is:

To create a scaled copy of a figure, all the side lengths in the original figure are multiplied by the same number. This number is called the scale factor.

In this example, the scale factor is 1.5, because , , and .

A solid of rotation is a three-dimensional figure formed by rotating a two-dimensional figure around a line called the axis of rotation.

In this diagram, the axis of rotation is the dashed line. The green triangle is rotated around the axis of rotation to form a solid of rotation.

A sphere is the set of all points in a three-dimensional space that are the same distance from a center point. All the cross-sections of a sphere are circles.

A figure has symmetry if there is a rigid transformation that takes it onto itself. (This does not include transformations that take every point back to its original position.)

A theorem is a statement that has been proved mathematically.

Trigonometric ratios relate the angles and sides of right triangles.

Three trigonometric ratios are sine, cosine, and tangent.