1. m1  61
m 2  29
m3  29
Prove Theorems Handout Answers
13. Given:  ABC is a right angle
Prove:  1 and  2 are complementary
Proof:
Statements
Reasons
a)  ABC is a right angle
a) Given
b) m ABC = 90
b) Def. of right angle
m
m
m
c)
ABC =
1+
2
c) Angle Addition Postulate
d) 90 = m 1 + m 2
d) Substitution Property
e)  1 and  2 are complementary
e) Def. of complementary
m 4  61
2. m5  59
m6  121
3. m7  109
m8  109
4. m9  31
14. Given:  1 is supplementary to
m10  59
 2 is supplementary to
Prove:
1  3
m11  90
Proof:
5. m12  58
Statements
m13  122
a)  1 is supp. to  2
m14  58
 2 is supp. to  3
b) m1  m2  180
m15  122
6. Jacob: Tomas did
m2  m3  180
not include  STP.
c) m1  m2  m2  m3
7. sometimes
d) m1  m3
8. always
e) 1  3
9. never
10. sometimes
11. never
12. sometimes
2
3
Reasons
a) Given
b) Def. of supp.
c) Substitution Property
d) Subtraction Property
e) Def. of congruent
15. Given: l  m
Prove:  1,  2,  3, and  4 are right angles
Proof:
Statements
Reasons
a) l  m
a) Given
b)  1,  2,  3, and  4
b) Def. of perpendicular
are right angles
16. Given: l  m
Prove:  1 and  2 are adjacent
1   2
Proof:
Statements
Reasons
a) l  m
a) Given
b)  1 and  2 are right angles b) Perpendicular lines form 4 right angles.
c) m1  90
c) Def. of right angle
m2  90
d) m1  m2
e) 1   2
f)  1 and  2 are adjacent
d) Substitution Property
e) Def. of congruent
f) Def. of adjacent angles
17. Given:  1 and  2 are right angles
Prove: 1   2
Proof:
Statements
Reasons
a)  1 and  2 are right angles a) Given
b) m1  90
b) Def. of right angle
m2  90
c) m1  m2
d) 1   2
1
2
c) Substitution Property
d) Def. of congruent
18. Given: 1   2
 1 and  2 form a linear pair
Prove:  1 and  2 are right angles
Proof:
Statements
Reasons
a) 1   2
a) Given
 1 &  2 form a linear pair
b)  1 and  2 are supp.
b) Supplement Theorem
c) m1  m2  180
c) Def. of supp.
d) m1  m1  180
d) Substitution Property
e) 2 m1  180
e) Combine Like Terms
f) m1  90
f) Division Property
g) m2  90
g) Substitution Property
h)  1 and  2 are right angles h) Def. of right angle
1
2