Section 2 5 Addition and Subtraction Properties Quick

Section 2. 5 Addition and Subtraction Properties

Quick Review n Define complementary n n Define supplementary n n Define congruent angles segments n Two angles are complementary if their sum is 90° Two angles are supplementary if their sum is 180° Two segments are congruent if their measures are equal. Two angles are congruent if they have the same measure.

Six New Properties and Theorems Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition Property) n Note that we first need to know that two segments are congruent, and then that we are adding the same segment to both of them.

Theorem 9: If an angle is added to two congruent angles, the sums are congruent (Addition Property) n Note that we first need to know that we have 2 congruent angles, then that we are adding the same angle to both

Cont… Theorem 10: If congruent segments are added to congruent segments, the sums are congruent. (Addition Property) n Note that first we need 2 congruent segments, then we need 2 different congruent segments to add

Cont… Theorem 11: If congruent angles are added to congruent angles, the sums are congruent. (Addition Property) n Note that first we need 2 congruent angles, then we need to add two different congruent angles

Cont… Theorem 12: If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. (Subtraction Property) n Note that we need to start with congruent angles or segments and then subtract the same angle or segment from both.

Cont… Theorem 12: Another example (Subtraction Property) n Note that we need to start with congruent angles or segments and then subtract the same angle or segment from both.

Cont… Theorem 13: If congruent segments (or angles) are subtracted from congruent segments (or angles), the differences are congruent. (Subtraction Property) n Note that we start with congruent segments or angles, and then subtract congruent segments or angles.

Using the Addition and Subtraction Properties n n An addition property is used when the segments or angles in the conclusion are greater than those in the given information A subtraction property is used when the segments or angles in the conclusion are smaller than those in the given information.

Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition Property) Given: Conclusion: Statements Reasons 1. Given 2. PQ = RS 2. If two segments are congruent, then they have the same measure 3. PQ + QR = RS + QR 3. Additive Property of Equality 4. PR = QS 4. Addition of Segments 5. If two segments have the same measure then they are congruent

How to use this theorem in a proof: Given: Conclusion: Statements Reasons 1. 2. Given 2. If a segment is subtracted from congruent segments, then the resulting segments are congruent. (Subtraction)