Chapter 2 Summary

Definitions

Perpendicular

Lines, rays or segments that intersect at right angles are perpendicular (⊥). (p.61)

Complementary angles

The measures of two complementary angles is 90° (a right angle).

Supplementary angles

The measures of two supplementary angles is 180° (a straight angle).

Opposite rays

Opposite rays are rays with a common endpoint and whose union is a line.

Vertical angles

Angles for which the rays forming one are opposite rays of the rays forming the other. So intersecting lines form two pairs of vertical angles.

Angle addition postulate: The measure of an angle made of two adjacent angles is the sum of the measures of the two adjacent angles.
Segment addition postulate: The measure of a segment made of two adjacent, collinear segments is the sum of the measures of the two adjacent segments.

Theorems 4-7 complementary/supplementary congruence: If angles are complementary/supplementary to the same/congruent angles, then they are congruent (p.76,77).
Theorems 8-11: addition property: If the same/congruent segments/angles are added to congruent segments/angles, the sums are congruent (p.82-83).
Theorems 12-13: subtraction property: If the same/congruent segments/angles are subtracted from congruent segments/angles, the differences are congruent (p-83-84).
Theorem 14: multiplication property: If segments/angles are congruent, their like multiples are congruent (p. 89).
Theorem 15: division property: If segments/angles are congruent, their like divisions are congruent (p. 90).
Theorem 16, 17: transitive property: x≅y and y≅z ⇒ x≅z (p. 95)
Algebra: You may use anything you know from basic algebra when talking about numbers (as opposed to geometric objects). So you must use geometry when talking about angles, but you can use algebra when talking about the measures of angles.
Substitution property: Ignore this! Instead, go to the "world of numbers" by making a statement about numbers and then use substitution in algebra.
Vertical angles are congruent.