1 / 24

2.5 Proving Statements about Line Segments

2.5 Proving Statements about Line Segments. Theorems are statements that can be proved. Theorem 2.1 Properties of Segment Congruence Reflexive AB ≌ AB All shapes are ≌ to them self Symmetric If AB ≌ CD, then CD ≌ AB Transitive If AB ≌ CD and CD ≌ EF, then AB ≌ EF.

wayne-neal
Download Presentation

2.5 Proving Statements about Line Segments

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 2.5 Proving Statements about Line Segments

  2. Theorems are statements that can be proved Theorem 2.1 Properties of Segment Congruence Reflexive AB ≌ AB All shapes are ≌ to them self Symmetric If AB ≌ CD, then CD ≌ AB Transitive If AB ≌ CD and CD ≌ EF, then AB ≌ EF

  3. How to write a Proof Proofs are formal statements with a conclusion based on given information. One type of proof is a two column proof. One column with statements numbered; the other column reasons that are numbered.

  4. Given: EF = GH Prove EG ≌ FH E F G H #1. EF = GH #1. Given

  5. Given: EF = GH Prove EG ≌ FH E F G H #1. EF = GH #1. Given #2. FG = FG #2. Reflexive Prop.

  6. Given: EF = GH Prove EG ≌ FH E F G H #1. EF = GH #1. Given #2. FG = FG #2. Reflexive Prop. #3. EF + FG = GH + FG #3. Add. Prop.

  7. Given: EF = GH Prove EG ≌ FH E F G H #1. EF = GH #1. Given #2. FG = FG #2. Reflexive Prop. #3. EF + FG = GH + FG #3. Add. Prop. #4. EG = EF + FG #4. FH = FG + GH

  8. Given: EF = GH Prove EG ≌ FH E F G H #1. EF = GH #1. Given #2. FG = FG #2. Reflexive Prop. #3. EF + FG = GH + FG #3. Add. Prop. #4. EG = EF + FG #4. Segment Add. FH = FG + GH

  9. Given: EF = GH Prove EG ≌ FH E F G H #1. EF = GH #1. Given #2. FG = FG #2. Reflexive Prop. #3. EF + FG = GH + FG #3. Add. Prop. #4. EG = EF + FG #4. Segment Add. FH = FG + GH #5. EG = FH #5. Subst. Prop.

  10. Given: EF = GH Prove EG ≌ FH E F G H #1. EF = GH #1. Given #2. FG = FG #2. Reflexive Prop. #3. EF + FG = GH + FG #3. Add. Prop. #4. EG = EF + FG #4. Segment Add. FH = FG + GH #5. EG = FH #5. Subst. Prop. #6. EG ≌ FH #6. Def. of ≌

  11. Given: RT ≌ WY; ST = WXR S TProve: RS ≌ XYW X Y #1. RT ≌ WY #1. Given

  12. Given: RT ≌ WY; ST = WX R S TProve: RS ≌ XY W X Y #1. RT ≌ WY #1. Given #2. RT = WY #2. Def. of ≌

  13. Given: RT ≌ WY; ST = WX R S TProve: RS ≌ XY W X Y #1. RT ≌ WY #1. Given #2. RT = WY #2. Def. of ≌ #3. RT = RS + ST #3. Segment Add. WY = WX + XY

  14. Given: RT ≌ WY; ST = WX R S TProve: RS ≌ XY W X Y #1. RT ≌ WY #1. Given #2. RT = WY #2. Def. of ≌ #3. RT = RS + ST #3. Segment Add. WY = WX + XY #4. RS + ST = WX + XY #4. Subst. Prop.

  15. Given: RT ≌ WY; ST = WX R S TProve: RS ≌ XY W X Y #1. RT ≌ WY #1. Given #2. RT = WY #2. Def. of ≌ #3. RT = RS + ST #3. Segment Add. WY = WX + XY #4. RS + ST = WX + XY #4. Subst. Prop. #5. ST = WX #5. Given

  16. Given: RT ≌ WY; ST = WX R S TProve: RS ≌ XY W X Y #1. RT ≌ WY #1. Given #2. RT = WY #2. Def. of ≌ #3. RT = RS + ST #3. Segment Add. WY = WX + XY #4. RS + ST = WX + XY #4. Subst. Prop. #5. ST = WX #5. Given #6. RS = XY #6. Subtract. Prop.

  17. Given: RT ≌ WY; ST = WX R S TProve: RS ≌ XY W X Y #1. RT ≌ WY #1. Given #2. RT = WY #2. Def. of ≌ #3. RT = RS + ST #3. Segment Add. WY = WX + XY #4. RS + ST = WX + XY #4. Subst. Prop. #5. ST = WX #5. Given #6. RS = XY #6. Subtract. Prop. #7. RS ≌ XY #7. Def. of ≌

  18. Given: x is the midpoint of MN and MX = RXProve: XN = RX #1. x is the midpoint of MN #1. Given

  19. Given: x is the midpoint of MN and MX = RXProve: XN = RX #1. x is the midpoint of MN #1. Given #2. XN = MX #2. Def. of midpoint

  20. Given: x is the midpoint of MN and MX = RXProve: XN = RX #1. x is the midpoint of MN #1. Given #2. XN = MX #2. Def. of midpoint #3. MX = RX #3. Given

  21. Given: x is the midpoint of MN and MX = RXProve: XN = RX #1. x is the midpoint of MN #1. Given #2. XN = MX #2. Def. of midpoint #3. MX = RX #3. Given #4. XN = RX #4. Transitive Prop.

  22. Something with Numbers If AB = BC and BC = CD, then find BC A D 3X – 1 2X + 3 B C

  23. Homework Page 105 # 6 - 11

  24. Homework Page 106 # 16 – 18, 21 - 22

More Related