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21 terms

Geometry Test Theorems and Postulates

Test friday! Check the book for the pictures.
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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.