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Lesson 2-6
Prove: If ABD and DBC form a linear
pair, then they are supplementary.
A
Objective – To prove conclusions involving
geometric figures.
Statement
•Definitions
•Postulates
•Properties
•Theorems
Hypothesis
(Given)
Conclusion
Linear Pair Theorem - If two angles form a linear
pair, then they are
supplementary.
1) ABD & DBC form
a linear pair.
 
2) BA & BC form
a straight
i h li
line
D
C
B
Reasons
Given
Def. of linear pair
3) mABC  180
Def. of straight angle
4) mABD  mDBC 
mABC
Angle Addition Post.
5) mABD  mDBC  180
Substitution (3 into 4)
6) ABD & DBC are suppl.
Def. of Suppl. Angles
Congruent Supplements Theorem
If two angles are supplementary
Congruent
Supplements - to the same angle, then they
are congruent.
Theorem
Prove: If ABE & EBC are suppl. &
EBC & DBC are suppl., then
ABE  DBC.
Statement
Right Angle
Congruence Theorem
All right angles are congruent.
If two angles are complementary
Congruent
Complements - to the same angle, then they
are congruent.
Theorem
Statement
1) 1 & 2 are right angles.
2) m1  90
m2  90
3) m1  m2
4) 1  2
2
1
Reasons
Given
Def. of right angles
Substitution (2 into 2)
Def. of  s
Reasons
E
B
C
D
1) ABE & EBC are suppl.
EBC & DBC are suppl.
2) mABE  mEBC  180
mEBC  mDBC  180
3) mABE  mEBC 
mEBC  mDBC
4) mEBC  mEBC
5) mABE  mDBC
Reflexive Property
Subtract Prop of Equal.
6) ABE  DBC
Def. of  s
Given
Def. of suppl. angles
Substitution (2 into 2)
Congruent Complements Theorem
Right Angle Congruence Theorem
Prove: If 1 is a rt. angle &
2 is a rt. angle, then 1  2.
A
Prove: If 1 & 2 are compl. &
2 & 3 are compl., then 1  3.
Statement
1) 1 & 2 are compl.
2 & 3 are compl.
2) m1  m2  90
m2  m3  90
1
2
3
Reasons
Given
Def. of compl. angles
3) m1  m2  m2  m3 Substitution (2 into 2)
4) m2  m2
Reflexive Property
5) m1  m3
Subtract Prop of Equal.
6) 1  3
Def. of  s
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
1
Lesson 2-6
Prove: If 2  3, then 1  4.
Statement
1) 2  3
2) 1 & 2 are linear pair.
3 & 4 are linear pair.
3) 1 & 2 are suppl.
3 & 4 are suppl.l
4) m1  m2  180
m3  m4  180
5) m1  m2  m3  m4
6) m2  m3
7) m1  m4
8) 1  4
1
2
3
4
Reasons
Given
Def. of linear pair
Linear Pair Theorem
Def of Suppl. Angles
Substitution (4 into 4)
Def. of  s
Subtract Prop of Equal.
Def. of  s
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
2