AMSCO'S Geometry. New York - Rye High School

Developing SkillsIn 3 and 4, in each case fill in the missing statement or reason in the proof to show that the conclusionis valid.13. Given: AB 4 BC and BC CD 4. Given: ma 3mb and mb 20Prove: CD 4AB Prove: ma 60Statements Reasons Statements Reasons11. AB 4 BC 1. 1. 1. Given.2. 4 4 2. 2. 2. Given.3. 4AB BC 3. 3. 3mb 60 3.4. BC CD 4. 4. 4. Transitive property of5. 4AB CD 5.equality.6. CD 4AB 6.The Multiplication and Division Postulates 127In 5–7, in each case write a proof to show that the conclusion is valid.15. Given: LM 2MN and MN 2 NPProve: LM > NP6. Given: 2(3a 4) 16Prove: a 47. Given: PQRS1, PQ 3QR, and QR 3 RSProve: PQ > RSApplying Skills8. On Monday, Melanie walked twice as far as on Tuesday. On Wednesday, she walked onethirdas far as on Monday and two-thirds as far as on Friday. Prove that Melanie walked asfar on Friday as she did on Tuesday.9. The library, the post office, the grocery store, and the bank are located in that order on thesame side of Main Street. The distance from the library to the post office is four times thedistance from the post office to the grocery store. The distance from the grocery store to thebank is three times the distance from the post office to the grocery store. Prove that the distancefrom the library to the post office is equal to the distance from the post office to thebank. (Think of Main Street as the line segment LPGB.)10. Explain why the following versions of Postulates 3.9 and 3.11 are valid:Doubles of congruent segments are congruent. Halves of congruent segments are congruent.Doubles of congruent angles are congruent. Halves of congruent angles are congruent.