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Proof #_____
Geometry AC
Name ____________________________
Theorem 2.1 If a segment has a midpoint then it is divided into two parts, each half the
original.
Given: M is the midpoint AB
Prove: AM 
1
2
Picture:
AB and MB  1 AB
2
Theorem 2.2 A bisector of an angle divides the angle into two angles, each of which has a
measure of half the given angle.
Reword the theorem in "if...then..." form. You can use your own words.
If __________________________________________________________________________,
then ________________________________________________________________________.
Which other theorem does this sound like?
_____________________________________________________________________________
____________________________________________________________________________.
Prove this theorem..
B
Given: XY bisects  BXA
Y
Prove:  BXY = ½m  BXA and
 YXA = ½m  BXA
X
A
Statements
1. Ray XY bisects  BXA
Justifications
1.
 BXY =  YXA
2.
3.  BXY +  YXA =  BXA
3.
4.  BXY +  BXY =  BXA
4.
2  BXY =  BXA
5.
2.
5.
6.
½ = ½
6.
7.
 BXY = ½  BXA
7.
8.
 YXA = ½  BXA
8.
Class Theorem 1. Every segment has exactly one bisector. Explain.
Class Theorem 2. Every angle has exactly one bisector. Explain.
Proof #_____
Geometry AC
Name ____________________________
Theorem 2.4: If two lines are perpendicular, then they form congruent adjacent angles.
(Perpendicular lines form congruent angles.)
Given:
Picture:
l
Prove:
m
1 2
Proof #_____
Geometry AC
Name ____________________________
Theorem 2.5: If two lines form congruent adjacent angles, then the lines are perpendicular.
Given:
Picture:
R
c
d
A
Prove:
Q
H
Proof #_____
Geometry AC
Name ____________________________
Theorem 2.6: If the exterior sides of two adjacent acute angles are perpendicular, then the
angles are complementary.
Given:
Picture:
O
P
1
Prove:
E
2
A
Proof #_____
Geometry AC
Name ____________________________
Theorem 2.7a: If two angles are supplementary to congruent angles then the two angles are
congruent.
(Two angles supplementary to congruent angles are congruent.)
Given:
Picture:
c
a
Prove:
b
d
Proof #_____
Geometry AC
Name ____________________________
Theorem 2.7b: If two angles are supplementary to the same angle, then they are congruent.
(Two angles supplementary to the same angle are congruent.)
Given:
Picture:
a
b
c
Prove:
Proof #_____
Geometry AC
Name ____________________________
Theorem 2.8a: If two angles are complementary to congruent angles, then the two angles are
congruent.
(Two angles complementary to congruent angles are congruent.)
Given:
Picture:
2
1
Prove:
3
4
Proof #_____
Geometry AC
Name ____________________________
Theorem 2.8b: If two angles are complementary to the same angle, then they are congruent.
(Two angles complementary to the same angle are congruent.)
Given:
Picture:
2 3
1
Prove:
Proof #_____
Geometry AC
Name ____________________________
Theorem 2.3: If two angles are vertical, then they are equal.
(Vertical angles are congruent.)
Given:
Picture:
D
1
A
Prove:
2
B
E
C
3
Proof #_____
Geometry AC
Name ____________________________
Class Theorem 3: If two angles are right angles, then they have equal measure.
(All right angles are equal.)
Given:
Prove:
Picture:
E
A