Download The Amazing Section 2.4

The Amazing Section
2.4
Congruent Supplements
and Complements
By: The amazing Jen Burke and the average
Kathleen Shedlock (Gimpy)
Supplementary Angles
 Two angles, whose sum is one hundred and eighty degrees.
70°
J
K
110°
70°
110°
180°
Theorem 4
 If angles are supplementary to the same angle, then they are
congruent.
C
T
65°
65°
A
115°
Short Form: suppl of the same
angle are congruent
Sample Problem
Given: <ACS suppl. <SCT
S
<ACS suppl. <STC
Prove: <SCT is congruent to
<STC
Statements
A
C
T
Reasons
1. <ACS suppl <SCT 1. Given
2. <ACS suppl.
2. Given
<STC
3. Suppl of the same
3. <SCT is congruent
< are
to <STC
congruent
Theorem 5
 If angles are supplementary to congruent angles, then they
are congruent.
F
R
45°
135°
135°
45°
Short Form: suppls of
congruent <s are congruent
O
G
Sample Problem
Given: <J suppl <B
<K suppl <S
<B <S
Prove: <J  <K
Statements
1. <J suppl <B
2. <K suppl <S
B
J
K S
3. <B
<S
4. <J  <K
Reasons
1. Given
2. Given
3. Given
4. Suppl of 
<s are 
Complementary Angles
• Two
angles, whose sum is ninety degrees.
A
B
25°
65°
90°
C
Theorem 6
 If angles are complementary to the same angle, then they are
congruent.
W
75°
O
75°
C
15°
Short Form: Compls of the
same < are 
Sample Problem
Given: <DIC compl <DSI
<CIS compl <DSI
Prove: <CIS  <DIC
D
C
Statements
Reasons
1. <DIC compl
<DSI
1. Given
2. <CIS compl
<DSI
I
S
2. Given
3. Compl of the
same < are 
3. <CIS <DIC
Theorem 7
•If angles are complementary to congruent angles, then they are
congruent.
Short Form: compls of  <s
are 
I
L
65°
25°
25°
E
F
65°
Sample Problem
1
Statements
Reasons
1. <1 compl <2
1. Given
2. <3 compl <4
2. Given
3. <4  <1
3. Given
4. <3  <2
4. Compls of  <s
are 
2
3
4
Given: <1 compl <2
<3 compl <4, <4 <1
Prove: <3  <2
Practice Problem #1
A
Given:
BC  DE
ACB  ADE
Prove: BAD  EAC
Statements
B
C
D
E
Reasons
Answer to previous slide
Statements
Reasons
1. BC  DE
1. Given
2. ACB  ADE
2. Given
3. BD  CE
3. Addition
4. ADE suppl ADC
ACB suppl ACD
4. If two adj <s form a st <.
They are suppl
5. ADC  ACD
5. Suppls of  <s are 
6.ACDisos
6. If 2 base <s of a are 
that isos
7. AC  AD
7. If  isos then legs 
8. BAD  EAC
8. SAS (3,5,7)
Practice Problem #2
V
K
O
Given: O is the midpt of VP and TK
OPT compl TOP
OTP compl TOP
VO  KO
Prove: VPT  KTP
Statements
T
P
Reasons
Answer to previous slide
Statements
Reasons
1.O mdpt of VP , TK
1. Given
2. OTP compl TOP
OPT compl TOP
3. OTP  OPT
2. Given
4. TP  TP
5.VO  KO
6. VP  KT
7.VPT  KTP
3. Compl of the same <
are 
4. Reflexive
5. Given
6. Multiplication
7. SAS (3,4,6)
Works Cited
"Isoscels Triangle Proof Example." Interactive Math Activities, Demonstrations,
Lessons with Definitions and Examples, Worksheets, Interactive Activities
and Other Resources. Web. 20 Jan. 2011.
West Irondequoit Central School District. Web. 20 Jan. 2011.
<http://www.westirondequoit.org>.
Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment
and Challenge. Evanston, IL: McDougal, Littell, 1991. Print.