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Addition & Subtraction Properties

Addition & Subtraction Properties. Lesson 2.5. 3 cm. 7 cm. 7 cm. A. B. C. D. In the diagram above, AB = CD. Do you think that AC = BD? Suppose that BC were 3cm. Would AC = BD? If AB = CD, does the length of BC have any effect on whether AC = BD?. Yes. Yes. No. Theorem 8:.

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Addition & Subtraction Properties

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  1. Addition & Subtraction Properties Lesson 2.5

  2. 3 cm 7 cm 7 cm A B C D • In the diagram above, AB = CD. • Do you think that AC = BD? • Suppose that BC were 3cm. Would AC = BD? • If AB = CD, does the length of BC have any effect on whether AC = BD? Yes Yes No

  3. Theorem 8: • If a segment is added to two congruent segments, the sums are congruent (Addition Property) P Q R S Given: PQ  RS Conclusion: PR  QS Proof:PQ  RS, so by definition of congruent segments, PQ = RS. Now, the Addition Property of Equality says that we may add QR to both sides, so PQ + QR = RS + QR. Substituting, we get PQ = QS. Therefore, PR QS by the definition of congruent segments.

  4. Theorem 9: • If an angle is added to two congruent angles, the sums are congruent. (Addition Property) Is EFH necessarily congruent to JFG?

  5. Theorem 10: • If congruent segments are added to congruent segments, the sums are congruent. (Addition Property) Do you think that KM is necessarily congruent to PO?

  6. Theorem 11: • If congruent angles are added to congruent angles, the sums are congruent. (Addition Property) Is TWX necessarily congruent to  TXW?

  7. Theorem 12: • If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. (Subtraction Property) If KO = KP and NO = RP, is KN = KR?

  8. Theorem 13: • If congruent segments (or angles) are subtracted from congruent segments (or angles) the differences are congruent. (Subtraction Property) • The only difference between Theorem 12 and 13 is that this one is plural.

  9. Given Given If  angles are subtracted from  angles, the differences are . (Subtraction property) 1. NOP  NPO 2. ROP  RPO 3. NOR  NPR

  10.  HEF is supp. to  EHG.  GFE is supp. to  FGH.  EHF   FGE  GHF   HGE  EHG  FGH  HEF  GFE Given Given Given Given If  angles are added to  angles, the sums are  . (Addition Property) Supplements of   s are  .

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