Perpendicular Lines & Planes, Inequality Postulates & Theorems, Triangle Inequality (Quiz #4)

Coplanar

Points, lines, or segments that lie in the same plane.

Noncoplanar

Points, lines, or segments that do not lie in the same plane.

Oblique line

A line that intersects a plane at exactly one point and is not perpendicular to the plane.

Three non-collinear points

Determine a unique plane.

Perpendicular line to a plane

A line that is perpendicular to every line in the plane passing through its foot.

Law of Trichotomy

For real numbers, exactly one of the following is true: a < b, a = b, a > b.

Transitive property for inequalities

If a > b and b > c, then a > c.

Substitution Property for Inequalities

A quantity may be substituted for its equal in any inequality.

Addition property for inequalities

If equal quantities are added to unequal quantities, then their sums are unequal in the same order.

Subtraction property for inequalities

If equal quantities are subtracted from equal quantities, then their differences are unequal in the same order.

Multiplication property for inequalities

Doubles of unequal quantities are unequal in the same order.

Division property for inequalities

If two quantities are unequal and they are multiplied or divided by a positive number, the resulting products are unequal in the same order.

Exterior angle of a triangle

An angle that is adjacent and supplementary to an interior angle of the triangle.

Exterior angle inequality theorem

The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

Side angle inequality theorem

If two sides of a triangle are not congruent, then the angles opposite them are also not congruent.

Converse of the side angle inequality theorem

If two angles of a triangle are not congruent, then the sides opposite them are also not congruent.

Foot of the line

The intersection point where a line intersects a plane.

Two intersecting lines

Determine a unique plane.

Given a plane and a point on the plane

There is exactly one line passing through the given point that is perpendicular to the plane.

Given a plane and a point not on the plane

There is exactly one line passing through that point which is perpendicular to the plane.

Interior angle

An angle formed inside the triangle by two sides.

A line and a point not on the line

determine a plane