2.4 Congruent
Supplements and
Complements
If <1 is a supplement to < A, and <2
is a supplement to <A, what can
you say about <s 1 and 2?
Theorem 4: If angles are
supplementary to the same angle,
then they are congruent.
Theorem 5: If angles are
supplementary to congruent
angles, then they are congruent.
Given:
<F is supp to <G
<H is supp to <J
<G ~
= <J
Conclusion: <F ~
= <H
<F is supp to <G
so <F + <G = 180
m<G = 180 - <F
m<F = 180 - <G
<H is supp to <J
m<H = 180 - <J
m<H = 180 - <G
(substitution)
<F ~
= <H Both have the same measure.
Theorem 6: If angles are complementary
to the same angle, then they are
congruent.
Theorem 7: If
angles are
complementary
to congruent
angles, then they
are congruent.
When studying the definitions of such terms as
right angle, bisector, midpoint and
perpendicular, you will master the concepts
more quickly if you try to understand the ideas
involved without memorizing definitions word
for word.
However, for Theorems 4-7 need to be
memorized in order to help remember concepts.
Look for the double
use of the word
complementary or
supplementary in a
problem.
A
Given: <A is comp. to <C
D
<DBC comp. <C
Conclusion:
Statement
B
Reason
1.<A comp <C
1. Given
2.<DBC comp <C
3.<A ~
= <DBC
2. Given
3. If angles are
complementary to the same angle, then
they are congruent.
C
Given:
Prove:
<6 ~
= <7
<5 ~
= <8
R O
5
S
6
7
E
8
Y
Statement
1.
2.
3.
4.
5.
6.
<6 = <7
<ROS is a straight <
<6 is supp. to <5
<OSE is a straight <.
<7 is supp. to <8.
<5 ~
= <8
Reason
1. Given
2. Assumed from diagram.
3. If 2 <‘s form a strt <,
they are supplementary.
4. Same as #2.
5. Same as #3
6. Supplements of ~
= <‘s
are ~
=.