2.5 Proving Statements about Line Segments
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2.5 Proving Statements about Line Segments
description
2.5 Proving Statements about Line Segments. Theorems are statements that can be proved. Theorem 2.1 Properties of Segment Congruence ReflexiveAB ≌ AB All shapes are ≌ to them self Symmetric If AB ≌ CD, then CD ≌ AB Transitive If AB ≌ CD and CD ≌ EF, then AB ≌ EF. - PowerPoint PPT Presentation
Transcript of 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 ≌ ABAll shapes are ≌ to them self
Symmetric If AB ≌ CD, then CD ≌ ABTransitive If AB ≌ CD and CD ≌ EF,
then AB ≌ EF
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.
Given: EF = GHProve EG ≌ FH E F G H
#1. EF = GH #1. Given
Given: EF = GHProve EG ≌ FH E F G H
#1. EF = GH #1. Given#2. FG = FG #2. Reflexive
Prop.
Given: EF = GHProve 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.
Given: EF = GHProve 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
Given: EF = GHProve 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
Given: EF = GHProve 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.
Given: EF = GHProve 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 ≌
Given: RT ≌ WY; ST = WX R S T
Prove: RS ≌ XY W X Y
#1. RT ≌ WY #1. Given
Given: RT ≌ WY; ST = WX R S T
Prove: RS ≌ XY W X Y
#1. RT ≌ WY #1. Given#2. RT = WY #2. Def. of ≌
Given: RT ≌ WY; ST = WX R S T
Prove: 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
Given: RT ≌ WY; ST = WX R S T
Prove: 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.
Given: RT ≌ WY; ST = WX R S T
Prove: 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
Given: RT ≌ WY; ST = WX R S T
Prove: 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.
Given: RT ≌ WY; ST = WX R S T
Prove: 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 ≌
Given: x is the midpoint of MN and MX = RXProve: XN = RX
#1. x is the midpoint of MN #1. Given
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
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
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.
Something with Numbers
If AB = BC and BC = CD, then find BCA D
3X – 1 2X + 3B C
Homework
Page 105# 6 - 11
Homework
Page 106# 16 – 18, 21 - 22
