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Section 2.5

Section 2.5. Addition and Subtraction Properties. Define complementary angles Define supplementary angles Define congruent segments Define congruent angles. Two angles are complementary if their sum is 90 ° Two angles are supplementary if their sum is 180°

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Section 2.5

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  1. Section 2.5 Addition and Subtraction Properties

  2. Define complementary angles Define supplementary angles Define congruent segments Define congruent angles 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. Quick Review

  3. Six New Properties and Theorems Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition Property) • 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.

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

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

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

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

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

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

  10. Using the Addition and Subtraction Properties • 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.

  11. Theorem 8: If a segment is added to two congruent segments, the sums are congruent. (Addition Property) Given: Conclusion: Statements Reasons 1. 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. 5. If two segments have the same measure then they are congruent

  12. How to use this theorem in a proof: Given: Conclusion:

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