question #1 given: m publish laureen singleton, modified 5 months...
TRANSCRIPT
QUESTION #1
GIVEN: m<1 = m<2
m<2 = 35
CONCLUSION: m<1 = 35
REASON: Transitive Property
QUESTION #2
GIVEN: EG = FG FG = GH
CONCLUSION: EG = GH
REASON: Transitive Property
QUESTION #3
GIVEN: X + 9 = 15
CONCLUSION: x = 6
REASON: Subtraction Property
QUESTION #4
GIVEN: JK = KL
MN = KL
CONCLUSION: JK = MN
REASON: Transitive Property
QUESTION #5
GIVEN: 7x = 35
CONCLUSION: x = 5
REASON: Division Property
QUESTION #6
GIVEN: m<3 = 75
m<4 = 75
CONCLUSION: m<3 + m<4 = 150
REASON: Addition Property
QUESTION #7
GIVEN: <1 = <2
<2 = <3
CONCLUSION: <1 = <3
REASON: Transitive Property
QUESTION #8
GIVEN: XY is a segment
CONCLUSION: XY = XY
REASON: Reflexive Property
QUESTION #9
GIVEN: 3x + y = 60
2x = y
CONCLUSION: 3x + 2x = 60
REASON: Substitution Property
QUESTION #10
GIVEN: <A = <B
CONCLUSION: <B = <A
REASON: Symmetric Property
GIVEN:16y + 8 = 13 – 24yPROVE: y = 1/5
Statement
1. 16y + 8 = 13 –24y
2. 40y + 8 = 13
3. 40y = 5
4. y = 1/5
Reason
1. Given
2. Addition Prop.
3. Subtraction Prop.
4. Division Prop.
GIVEN: <1 + <2 = 120<1 = 100
PROVE: m<2 = 20
Statement
1. m<1 + m<2 = 120
2. m<1 = 100
3. 100 + m<2 = 120
4. m<2 = 20
Reason
1. Given
2. Given
3. Substitution
4. Subtraction Prop.
GIVEN: m<1 = 60; m<2 = 60m<1 + m<3 = 120m<4 + m<2 = 120
PROVE: m<3 = m<4
Statement1. m<1 + m<3 = 120
2. m<1 = 60
3. m<3 = 60
4. m<4 + m<2 = 120
5. m<2 = 60
6. m<4 = 60
7. m<3 = m<4
Reason1. Given
2. Given
3. Subtraction Prop.
4. Given
5. Given
6. Subtraction Prop.
7. Transitive Prop.
GIVEN: m<1 + m<2 = 180m<2 + m<3 = 180
PROVE: m<2 = m<3Statement
1. m<1 +m<2 =180
2. m<2 + m<3 = 180
3. m<1 + m<2 = m<2 + m<3
4. m<2 = m<2
5. m<1 = m<3
Reason1. Given
2. Given
3. Transitive Prop.
4. Reflexive Prop.
5. Subtraction Prop.
GIVEN: X lies between A and B; AX = 5; XB = 3
PROVE: AB = 8
STATEMENTS
1. X lies between A and B.
2. AX + XB = AB
3. AX = 5; XB = 3
4. 5 + 3 = AB
5. 8 = AB
6. AB = 8
REASONS
1. Given
2. Segment Addition Post.
3. Given
4. Substitution Property
5. Substitution Property
6. Symmetric Property
GIVEN: S lies between points R and TPROVE: ST = RT - RS
STATEMENTS
1. S lies between R and T.
2. RS + ST = RT
3. ST = RT - RS
REASONS
1. Given
2. Segment Addition Postulate
3. Subtraction Property of Equality
GIVEN: m<AOC = m<BODPROVE: m<1 = m<3
STATEMENTS
1. m< AOC = m<BOD
2. m<AOC = m<1 + m<2; m<BOD = m<2 + m<3
3. m<1 + m<2 = m<2 + m<3
4. m<2 = m<2
5. m<1 = m<3
REASONS
1. Given
2. Angle Addition Postulate
3. Substitution Property
4. Reflexive Property
5. Subtraction Property
GIVEN: Ray XS bisects <RXT;m<RXS = j
PROVE: m<RXT = 2j
STATEMENTS
1. XS bisects <RXT.
2. <RXS ≅ <SXT
3. m<RXS = m<SXT
4. m<RXS = j
5. m<SXT = j
6. m<RXT = m<RXS + m<SXT
7. m<RXT = j + j or 2j
REASONS
1. Given
2. Def. of < bisector
3. Def. of ≅ <‘s
4. Given
5. Substitution Property
6. Angle Addition Thm.
7. Substitution Property
GIVEN: B lies between A and C;C lies between B and D;AC = BD
PROVE: AB = CD STATEMENTS
1. B lies between A and C.
2. AB + BC = AC
3. C lies between B and D.
4. BC + CD = BD
5. AC = BD
6. AB + BC = BC + CD
7. AB = CD
REASONS
1. Given
2. Segment Addition Post.
3. Given
4. Segment Addition Post.
5. Given
6. Substitution Property
7. Subtraction Property
GIVEN: <2 ≅ <3PROVE: <1 ≅ <4
STATEMENTS
1. <1 ≅ <2
2. <2 ≅ <3
3. <3 ≅ < 4
4. <1 ≅ < 4
REASONS
1. Vertical <‘s are ≅.
2. Given
3. Vertical <‘s are ≅
4. Transitive Property (used twice).
GIVEN: Ray BX is the bisector of <ABCPROVE: m<ABX = ½m<ABC;
m<XBC = ½m<ABC
STATEMENTS
1. BX is the bisector of <ABC.
2. <ABX ≅ <XBC
3. m<ABX + m<XBC = m<ABC
4. 2m<ABX = m<ABC
5. m<ABX = ½m<ABC
6. m<XBC = ½m<ABC
REASONS
1. Given
2. Def. of a bisector
3. Angle Addition Postulate
4. Substitution Property
5. Division Property
6. Substitution Property