The Amazing Section 2.4

1
The Amazing Section 2.4

• Congruent Supplements and Complements

By The amazing Jen Burke and the average
Kathleen Shedlock (Gimpy?)
2
Supplementary Angles

• Two angles, whose sum is one hundred and eighty
  degrees.

70
K
110
J
70
110
180
3
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
4
Sample Problem
Given ltACS suppl. ltSCT ltACS suppl. ltSTC Prove
ltSCT is congruent to ltSTC
S
Statements Reasons
1. ltACS suppl ltSCT 2. ltACS suppl. ltSTC 3. ltSCT is congruent to ltSTC 1. Given 2. Given 3. Suppl of the same lt are congruent
T
A
C
5
Theorem 5

• If angles are supplementary to congruent angles,
  then they are congruent.

F
R
45
135
135
45
Short Form suppls of congruent lts are congruent
G
O
6
Sample Problem
Given ltJ suppl ltB ltK suppl ltS ltB ltS
Prove ltJ ltK
Statements
Reasons
1. ltJ suppl ltB
1. Given
2. ltK suppl ltS
2. Given
J
B
3. ltB ltS
3. Given
K
S
4. ltJ ltK
4. Suppl of lts are
7
Complementary Angles

• Two angles, whose sum is ninety degrees.

A
B
25
65
90
C
8
Theorem 6

• If angles are complementary to the same angle,
  then they are congruent.

W
75
O
75
C
Short Form Compls of the same lt are
15
9
Sample Problem
Given ltDIC compl ltDSI ltCIS compl ltDSI Prove
ltCIS ltDIC
D
Statements
Reasons
C

1. ltDIC compl ltDSI
2. ltCIS compl ltDSI
3. ltCIS ltDIC

1. Given
2. Given
3. Compl of the same lt are

S
I
10
Theorem 7

• If angles are complementary to congruent angles,
  then they are congruent.

Short Form compls of lts are
I
L
65
25
25
65
E
F
11
Sample Problem
1
2
Statements
Reasons
3
4

1. lt1 compl lt2
2. lt3 compl lt4
3. lt4 lt1
4. lt3 lt2

1. Given
2. Given
3. Given
4. Compls of lts are

Given lt1 compl lt2 lt3 compl lt4, lt4 lt1 Prove lt3
lt2
12
Practice Problem 1

A
Given
Prove
Statements
Reasons
B
E
C
D
13
Answer to previous slide
Statements
Reasons

• 1.
• 2.
• 3.
• 4.
• 5.
• 6. isos

• Given
• Given
• Addition
• If two adj lts form a st lt. They are suppl
• Suppls of lts are
• If 2 base lts of a are that isos
• If isos then legs
• SAS (3,5,7)

7. 8.
14
Practice Problem 2
Given
V
K
O
Prove
Statements
Reasons
T
P
15
Answer to previous slide
Statements
Reasons

1. Given
2. Given
3. Compl of the same lt are
4. Reflexive
5. Given
6. Multiplication
7. SAS (3,4,6)

16
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.  lthttp//www.westirondequoit.
orggt. Rhoad, Richard, George Milauskas, and
Robert Whipple. Geometry for Enjoyment and
Challenge. Evanston, IL McDougal, Littell, 1991.
Print.