Geometry Chapter 3 Vocabulary: Parallel Lines and Planes

Vocabulary flashcards covering lines, planes, transversals, angle relationships, triangle theorems, polygon properties, technical drawings, and types of reasoning from Chapter 3.

Parallel lines

Coplanar lines that do not intersect.

Skew lines

Noncoplanar lines that are neither parallel nor intersecting.

Parallel planes

Planes that do not intersect.

Line parallel to a plane

A line and a plane that do not intersect.

Theorem 3-1

If two parallel planes are cut by a third plane, then the lines of intersection are parallel.

Transversal

A line that intersects two or more coplanar lines in different points.

Alternate interior angles

Two nonadjacent interior angles on opposite sides of a transversal.

Same-side interior angles

Two interior angles on the same side of a transversal.

Corresponding angles

Two angles in corresponding positions relative to two lines cut by a transversal.

Postulate 10

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Theorem 3-2

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

Theorem 3-3

If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

Theorem 3-4

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.

Postulate 11

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Theorem 3-5

If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Theorem 3-6

If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

Theorem 3-7

In a plane, two lines perpendicular to the same line are parallel.

Theorem 3-8

Through a point outside a line, there is exactly one line parallel to the given line.

Theorem 3-9

Through a point outside a line, there is exactly one line perpendicular to the given line.

Theorem 3-10

Two lines parallel to a third line are parallel to each other.

Orthographic projection

A set of projections of an object into three planes perpendicular to one another, consisting of a top view, front view, and side view.

Isometric drawing

A two-dimensional representation of a three-dimensional object viewed at an angle that shows the top, front, and one side simultaneously without perspective, preserving congruence of sides.

Scalene triangle

A triangle with no sides congruent.

Isosceles triangle

A triangle with at least two sides congruent.

Equilateral triangle

A triangle with all sides congruent.

Acute triangle

A triangle with three acute angles.

Obtuse triangle

A triangle with one obtuse angle.

Right triangle

A triangle with one right angle.

Equiangular triangle

A triangle with all angles congruent.

Auxiliary line

A line, ray, or segment added to a diagram to help in a proof.

Theorem 3-11

The sum of the measures of the angles of a triangle is $180^\text{o}$.

Corollary

A statement that can be proved easily by applying a theorem.

Exterior angle of a triangle

An angle formed when one side of a triangle is extended beyond a vertex.

Remote interior angles

The two interior angles of a triangle that are not adjacent to a given exterior angle.

Theorem 3-12

The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.

Polygon

A figure formed by coplanar segments (sides) such that each segment intersects exactly two other segments, one at each endpoint, and no two segments with a common endpoint are collinear.

Convex polygon

A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.

Diagonal of a polygon

A segment joining two nonconsecutive vertices of a polygon.

Regular polygon

A polygon that is both equiangular and equilateral.

Theorem 3-13

The sum of the measures of the angles of a convex polygon with $n$ sides is $(n - 2) \times 180^\text{o}$.

Theorem 3-14

The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is $360^\text{o}$.

Deductive reasoning

A process of reasoning to a conclusion based on accepted statements (definitions, postulates, previous theorems, corollaries, and given information); the conclusion must be true if the hypotheses are true.

Inductive reasoning

A process of reasoning to a conclusion based on several past observations; the conclusion is probably true, but not necessarily true.