Addition Properties

Theorem-If a segment is added to two congruent segments, the sums are congruent.(Addition Property)

Theorem-If an angle is added to two congruent angles, the sums are congruent.(Addition Property)

Theorem-If congruent segments are added to congruent segments, the sums are congruent.(Addition Property)

Theorem-If congruent angles are added to congruent angles, then the sums are congruent.(Addition Property)

Subtraction Properties

Theorem-If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent.(Subtraction Property)

Theorem-if congruent segments (or angles) are subtracted from congruent segments (or angles), the differences are congruent.(Subtraction property)

1. An addition  property is used when the segments or angles in the conclusion are greater than those in the given information.

2. A subtraction property is used when the segments or angles in the conclusion are smaller than those in the given information.