Lesson 2.5.  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.

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Presentation transcript:

Lesson 2.5

 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? ACBD Yes 7 cm Yes No 3 cm

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

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

 If congruent segments are added to congruent segments, the sums are congruent. (Addition Property) Do you think that KM is necessarily congruent to PO?

 If congruent angles are added to congruent angles, the sums are congruent. (Addition Property) Is  TWX necessarily congruent to  TXW?

 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?

 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.

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

1.  HEF is supp. to  EHG. 2.  GFE is supp. to  FGH. 3.  EHF   FGE 4.  GHF   HGE 5.  EHG   FGH 6.  HEF   GFE 1.Given 2.Given 3.Given 4.Given 5.If  angles are added to  angles, the sums are . (Addition Property) 6.Supplements of   s are .