Geometry Test Theorems and Postulates

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Test friday! Check the book for the pictures.

right angles congruence theorem

all right angles are congruent

congruent supplements theorem

if two angles are supplementary to the same angle (or to congruent angles), then they are congruent.

congruent complements theorem

if two angles are complementary to the same angle (or to congruent angles), then they are congruent. for example: if two angles are complementary to the same angle (or to congruent angles), then they are congruent.

linear pair postulate

if two angles form a linear pair, then they are supplementary.

Vertical Angles Congruence Theorem

Vertical angles are congruent.

Parallel Postulate

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

Perpendicular Postulate

If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

Transversal

A line that interesects two or more coplanar lines at different points.

Corresponding Angles

Two angles are corresponding angles if they have corresponding positions.

Alternate Interior Angles

Two angles are alternate interior angles if they lie between the two lines and on opposite sides of the transversal.

Alternate Exterior Angles

They lie outside the two lines and on opposite sides of the transversal.

Consecutive Interior Angles

They lie between the two lines and on the same side of the transversal.

Corresponding Angles Postulate

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

Alternate Interior Angles Theorem

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

Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

Corresponding Angles Converse

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

Alternate Interior Angles Converse

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

Alternate Exterior Angles Converse

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

Consecutive Interior Angles Converse

If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.

Transitive Property of Parallel Lines

If two lines are parallel to the same line, then they are parallel to each other.

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