Chp 9 and 10 geometry vocabulary mcdogal littel

Geometric mean

For two positive numbers a and b, the positive number x such that a/x = x/b.

Pythagorean theorem

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Pythagorean triple

A set of three positive integers a, b, and c that satisfy the equation a^2 + b^2 = c^2.

Special right triangles

Right triangles whose angle measures are exactly 45-45-90 or 30-60-90 degrees, which possess specific, predictable ratios between their side lengths.

Trigonometric ratio

A ratio of the lengths of two sides in a right triangle.

Sine

A trigonometric ratio for acute angles that is the ratio of the length of the opposite leg to the length of the hypotenuse (opp/hyp).

Cosine

A trigonometric ratio for acute angles that is the ratio of the length of the adjacent leg to the length of the hypotenuse (adj/hyp).

Tangent (trigonometry)

A trigonometric ratio for acute angles that is the ratio of the length of the opposite leg to the length of the adjacent leg (opp/adj).

Angle of elevation

The angle that an upward line of sight makes with a horizontal line.

Magnitude of a vector

The length of a vector, representing the distance from its initial point to its terminal point.

Direction of a vector

The angle a vector makes with a horizontal line or the x-axis, typically measured counterclockwise.

Circle

The set of all points in a plane that are equidistant from a given point called the center.

Radius

A segment whose endpoints are the center and any point on the circle; it is also the distance from the center to a point on the circle.

Congruent

Figures that have exactly the same size and shape.

Diameter

A chord that contains the center of the circle; it is also the distance across a circle through its center.

Chord

A line segment whose endpoints both lie on the circle.

Secant

A line that intersects a circle in exactly two points.

Tangent (geometry)

A line in the plane of a circle that intersects the circle in exactly one point.

Point of tangency

The single point at which a tangent line intersects a circle.

Concentric circles

Coplanar circles that share a common center.

Minor arc

An arc of a circle whose measure is strictly less than 180 degrees.

Major arc

An arc of a circle whose measure is strictly greater than 180 degrees.

Inscribed angle

An angle whose vertex lies on a circle and whose sides contain chords of the circle.

Intercepted arc

The arc that lies in the interior of an inscribed angle and has endpoints on the angle.

Inscribed polygon

A polygon whose vertices all lie exactly on a circle.

Circumscribed circle

The circle that perfectly contains all the vertices of an inscribed polygon.