Honors Geometry
Proofs Involving Angles
Here are some suggestions that
may help you when doing proofs.
1. Your given information
(hypothesis) becomes your first
statement. What you need to
prove (conclusion) is your last
statement.
2. Reason backwards when
possible.
3. Consider each piece of given
information separately and make
any conclusion that follows.
4. In most proofs, you will have to write
out at least one statement based on the
figure. You may look for ONLY the
following:
a)Angle Addition postulate
b)Segment Addition Postulate
c)Linear pairs
d)Vertical Angles
5. In most proofs, you will use the
Substitution Property shortly after
the statement you make based on
the figure (usually within two
steps). Watch for it!
Right Angle Theorem (RAT)
All right angles are congruent.
If _______________________
two angles are right angles
the angles are congruent.
then_____________________
Given: _______________
A and  B are right angles
A  B
Prove:_______________
1.  A and  B are right angles
A
B
1.Given
2. m  A  90, m  B  90 2. Def. of
right angles
3.  A   B
3. Substitution
Congruent Supplements Theorem
If two angles are supplements of
the same or congruent angles,
then they are congruent.
1 .  1 and  2 are supplement ary
1 . Given
 3 and  4 are supplement ary
1   3
2. m  1  m  2  180
2. Def. of supp.
m  3  m  4  180
3. m  1  m  2  m  3  m  4
4.
2  4
3. substituti
4. subtractio
on prop.
n property
1
2
Vertical angles are the
4
3
nonadjacent angles
formed when two lines intersect.
Vertical Angle Theorem (VAT):
Vertical angles are congruent.
1) 1 and  2 are vert. angles
1) Given
2 )  1 and  3 are a L.P.
2) Def. of L.P.
 2 and  3 are a L.P.
3 ) 1 and  3 are supp.
3) L. P. Post.
 2 and  3 are supp.
4)
1   2
4) Cong. Supp. Thrm.
1)  1 and  2 are complement ary
1) Given
2 ) m  1  m  2  90
2 ) Def. of Comp.
3 )  1 &  3 are vert. angles
3 ) Def. of vert. angles
4 ) 1   3
) m  3  m  2  90
)  3 and  2 are complement ary
4 ) Vert. Angles theorem
5 ) substituti on
) Def. of Comp.