1. QUESTION #1
GIVEN: m<1 = m<2 m<2 = 35 CONCLUSION: m<1 = 35 REASON: Transitive Property

2. QUESTION #2
GIVEN: EG = FG FG = GH CONCLUSION: EG = GH REASON: Transitive Property

3. QUESTION #3
GIVEN: X + 9 = 15 CONCLUSION: x = 6 REASON: Subtraction Property

4. QUESTION #4
GIVEN: JK = KL MN = KL CONCLUSION: JK = MN REASON: Transitive Property

5. QUESTION #5
GIVEN: 7x = 35 CONCLUSION: x = 5 REASON: Division Property

6. QUESTION #6
GIVEN: m<3 = 75 m<4 = 75 CONCLUSION: m<3 + m<4 = 150 REASON: Addition Property

7. QUESTION #7
GIVEN: <1 = <2 <2 = <3 CONCLUSION: <1 = <3 REASON: Transitive Property

8. QUESTION #8
GIVEN: XY is a segment CONCLUSION: XY = XY REASON: Reflexive Property

9. QUESTION #9
GIVEN: 3x + y = 60 2x = y CONCLUSION: 3x + 2x = 60 REASON: Substitution Property

10. QUESTION #10
GIVEN: <A = <B CONCLUSION: <B = <A REASON: Symmetric Property

11. GIVEN:16y + 8 = 13 – 24y PROVE: y = 1/5
Statement
Reason
16y + 8 = 13 –24y
40y + 8 = 13
40y = 5
y = 1/5
Given
Addition Prop.
Subtraction Prop.
Division Prop.

12. GIVEN: <1 + <2 = 120 <1 = 100 PROVE: m<2 = 20
Statement
Reason
m<1 + m<2 = 120
m<1 = 100
100 + m<2 = 120
m<2 = 20
Given
Substitution
Subtraction Prop.

13. GIVEN: m<1 = 60; m<2 = 60. m<1 + m<3 = 120
GIVEN: m<1 = 60; m<2 = 60 m<1 + m<3 = m<4 + m<2 = 120 PROVE: m<3 = m<4
Statement
Reason
m<1 + m<3 = 120
m<1 = 60
m<3 = 60
m<4 + m<2 = 120
m<2 = 60
m<4 = 60
m<3 = m<4
Given
Subtraction Prop.
Transitive Prop.

14. GIVEN: m<1 + m<2 = 180 m<2 + m<3 = 180 PROVE: m<2 = m<3
Statement
Reason
m<1 +m<2 =180
m<2 + m<3 = 180
m<1 + m<2 = m<2 + m<3
m<2 = m<2
m<1 = m<3
Given
Transitive Prop.
Reflexive Prop.
Subtraction Prop.

15. GIVEN: X lies between A and B; AX = 5; XB = 3 PROVE: AB = 8
STATEMENTS
X lies between A and B.
AX + XB = AB
AX = 5; XB = 3
5 + 3 = AB
8 = AB
AB = 8
REASONS
Given
Segment Addition Post.
Substitution Property
Symmetric Property

16. GIVEN: S lies between points R and T PROVE: ST = RT - RS
STATEMENTS
S lies between R and T.
RS + ST = RT
ST = RT - RS
REASONS
Given
Segment Addition Postulate
Subtraction Property of Equality

17. GIVEN: m<AOC = m<BOD PROVE: m<1 = m<3
STATEMENTS
m< AOC = m<BOD
m<AOC = m<1 + m<2; m<BOD = m<2 + m<3
m<1 + m<2 = m<2 + m<3
m<2 = m<2
m<1 = m<3
REASONS
Given
Angle Addition Postulate
Substitution Property
Reflexive Property
Subtraction Property

18. GIVEN: Ray XS bisects <RXT; m<RXS = j PROVE: m<RXT = 2j
STATEMENTS
XS bisects <RXT.
<RXS ≅ <SXT
m<RXS = m<SXT
m<RXS = j
m<SXT = j
m<RXT = m<RXS + m<SXT
m<RXT = j + j or 2j
REASONS
Given
Def. of < bisector
Def. of ≅ <‘s
Substitution Property
Angle Addition Thm.

19. GIVEN: B lies between A and C;. C lies between B and D;
GIVEN: B lies between A and C; C lies between B and D; AC = BD PROVE: AB = CD
STATEMENTS
B lies between A and C.
AB + BC = AC
C lies between B and D.
BC + CD = BD
AC = BD
AB + BC = BC + CD
AB = CD
REASONS
Given
Segment Addition Post.
Substitution Property
Subtraction Property

20. GIVEN: <2 ≅ <3 PROVE: <1 ≅ <4
STATEMENTS
<1 ≅ <2
<2 ≅ <3
<3 ≅ < 4
<1 ≅ < 4
REASONS
Vertical <‘s are ≅.
Given
Vertical <‘s are ≅
Transitive Property (used twice).

21. GIVEN: Ray BX is the bisector of <ABC PROVE: m<ABX = ½m<ABC;
GIVEN: Ray BX is the bisector of <ABC PROVE: m<ABX = ½m<ABC; m<XBC = ½m<ABC
STATEMENTS
BX is the bisector of <ABC.
<ABX ≅ <XBC
m<ABX + m<XBC = m<ABC
2m<ABX = m<ABC
m<ABX = ½m<ABC
m<XBC = ½m<ABC
REASONS
Given
Def. of a bisector
Angle Addition Postulate
Substitution Property
Division Property