Geometry - Angle Relationships
Linear Pair
A pair of adjacent angles whose non-adjacent sides form opposite rays. (And these angles are also supplementary.)
Vertical Angles
A pair of opposite congruent angles formed by intersecting lines.
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the alternate interior 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 Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Lines Perpendicular to a Transversal Theorem
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
Complementary Angles
Two angles whose sum is 90 degrees.
Alternate Exterior Angles Converse
Two lines are cut by a transversal, if the pairs of alternate exterior angles are congruent, then the two lines are parallel.
Alternate Interior Angles Converse
Two lines are cut by a transversal, if the pairs of alternate interior angles are congruent, then the two lines are parallel.
Consecutive Interior Angles Converse
Two lines are cut by a transversal, if the pairs of consecutive interior angles are supplementary, then the two lines are parallel.
Corresponding Angles Converse
Two lines are cut by a transversal, if the pairs of corresponding angles are congruent, then the two lines are parallel.
Vertical Angles Congruence Theorem
Vertical angles are congruent
Lines Perpendicular to a Transversal Theorem
Which theorem can be use to prove m is parallel to n, given that m is perpendicular to p and n is perpendicular to p?
Perpendicular Transversal Theorem
Which theorem can be used to prove j is perpendicular to k, given that j is perpendicular to h and h is parallel to k?
Linear Pair Postulate
Which theorem/postulate proves angle 1 and angle 3 or angle 5 and angle 6 are supplementary?
Vertical Angles Congruence Theorem
Which theorem/postulate proves angle 3 is congruent to angle 2 or angle 5 congruent to angle 8?
Supplementary Angles
Angles whose sum is 180 degrees.
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Corresponding Angles Converse
If angle 1 is congruent to angle 5, which theorem/postulate proves line a is parallel to line m?
Alternate Exterior Angles Converse
If angle 1 is congruent to angle 8, which theorem/postulate proves line a is parallel to line m?
Consecutive Interior Angles Converse
If angle 4 and angle 6 are supplementary, which theorem/postulate proves line a is parallel to line m?
Alternate Interior Angles Converse
If angle 4 is congruent to angle 5, which theorem/postulate proves line a is parallel to line m?
Alternate Exterior Angles Theorem
If line a is parallel to line m, which theorem/postulate proves angle 1 is congruent to angle 8 or angle 2 congruent to angle 7?
Alternate Interior Angles Theorem
If line a is parallel to line m, which theorem/postulate proves angle 3 is congruent to angle 6 or angle 5 congruent to angle 4?
Corresponding Angles Postulate
If line a is parallel to line m, which theorem/postulate proves angle 3 is congruent to angle 7 or angle 2 congruent to angle 6?
Consecutive Interior Angles Theorem
If line a is parallel to line m, which theorem/postulate proves angle 4 and angle 6 or angle 3 and angle 5 are supplementary?
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary
Alternate Interior Angles
Angles between two lines and on opposite sides of a transversal.
Consecutive Interior Angles
Angles that are on the same side of the transversal and inside the two lines.
Corresponding Angles
Angles that lie on the same side of the transversal and in corresponding positions.
Alternate Exterior Angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.