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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.

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2.5 Proving Statements about Line Segments

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  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

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