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Chapter 4 Theorems
Theorem 4.1
All right angles are congruent.
Theorem 4.2
If two angles are adjacent and supplementary, then they form a linear pair.
Theorem 4.3
Angles that form a linear pair are supplementary.
Theorem 4.4
If one angle of a linear pair is a right angle, then the other angle is also a right angle.
Theorem 4.5
Vertical Angle Theorem. Vertical angles are congruent.
Theorem 4.6
Congruent supplementary angles are right angles.
Theorem 4.7
Angle Bisector Theorem. If AB bisects ∠CAD, then m∠CAB = ½ m∠CAD.
Chapter 5 Theorems
Theorem 5.1 Congruent Segment Bisector Theorem. If two congruent segments are bisected, then
the four resulting segments are congruent.
Theorem 5.2 Supplements of congruent angles are congruent.
Theorem 5.3 Complements of congruent angles are congruent.
Theorem 5.4 Adjacent Angle Sum Theorem. If two adjacent angles are congruent to another pair
of adjacent angles, then the larger angles formed are congruent.
Theorem 5.5 Adjacent Angle Portion Theorem. If two angles, one in each of two pairs of adjacent
angles, are congruent, and the larger angles formed are also congruent, then the other two angles
are congruent.
Theorem 5.6 Alternate Exterior Angle Theorem. Two lines intersected by a transversal are
parallel if and only if the alternate exterior angles are congruent.
Theorem 5.7 Corresponding Angle Theorem. Two lines intersected by a transversal are parallel if
and only if the corresponding angles are congruent.
Theorem 5.8 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular
to the other also.
Theorem 5.9 If two coplanar lines are perpendicular to the same line, then they are parallel to
each other.
Theorem 5.10
The sum of the measures of the angles of any triangle is 180°.
Theorem 5.11
If tow angles of one triangle are congruent to two angles of another triangle, then the third angles
are also congruent.
Theorem 5.12
The acute angles of a right triangle are complementary.
Postulates.
Postulate 5.1 Parallel postulate. Two lines intersected by a transversal are parallel if and only if
the alternate interior angles are congruent.
Postulate 5.2 Given a line and a point not on the line, there is exactly one line passing through the
point that is parallel to the given line.