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Advanced Geometry
Learning Target 2.2: Proving Parallel Line Theorems
Definition of an Angle Bisector
A ray whose endpoint is the vertex of an angle and is located on the interior of the angle that separates the angle
into two angles of equal measure.
Angle Addition Postulate
If R is in the interior of PQS , then mPQR  mRQS  mPQS .
If mPQR  mRQS  mPQS , then R is in the interior of PQS .
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
Linear Pair Theore m
If two angles form a linear pair, then they are supplementary angles.
Proof
Given:
and
form a linear pair
Prove:
and
are supplementary
Right Angle Pair Theore m
If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.
Proof
Given:
is a right angle
Prove:
and
are complementary
Vertical Angles Theore m
If two angles are vertical angles, then they are congruent.
Proof
Given:
and
are vertical angles
Prove:
Right Angle Theore ms
 Perpendicular lines intersect to form four right angles.
 All right angles are congruent.
 Perpendicular lines form congruent adjacent angles.
 If two angles are congruent and supplementary, then each angle is a right angle.
 If two congruent angles form a linear pair, then they are right angles.
Alte rnate Inte rior Angles Theore m
If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
Proof
Given:
Prove:
Same Side Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of same side interior angles is supplementary.
Proof
Given:
Prove:
and
are supplementary
Alte rnate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.
Proof
Given:
Prove: