4.3 Proving 4.3 Proving Triangles are Triangles are Congruent Congruent Side-Side-Side Side-Side-Side Side-Angle-Side Side-Angle-Side
4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.
Dec 24, 2015
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4.3 Proving Triangles are 4.3 Proving Triangles are Congruent Congruent
Side-Side-SideSide-Side-Side
Side-Angle-SideSide-Angle-Side
Side-Side-Side
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
X
Y
Z A B
C
XYZBCA
Side-Angle-Side
If two sides and an angle between the sides are congruent in two different triangles, then the triangles are congruent.
KL
M
C
D
H
HDCKLM
Name the congruent Triangles
K
M PL
N
Name the congruent Triangles
K
M PL
N
NMPKLM
Prove YWXVWZ
V
WZ
X
Y
Prove
#1. #1. Given
#2. #2. Vertical angles congruent
#3. #3. Given
#4. #4. S.A.S.
(side-angle-side)
YWXVWZ
V
WZ
X
Y
WYVW
Prove
#1. #1. Given
#2. #2. Vertical angles congruent
#3. #3. Given
#4. #4. S.A.S.
(side-angle-side)
YWXVWZ
V
WZ
X
Y
WYVW YWXVWZ
Prove
#1. #1. Given
#2. #2. Vertical angles congruent
#3. #3. Given
#4. #4. S.A.S.
(side-angle-side)
YWXVWZ
V
WZ
X
Y
WYVW YWXVWZ
Prove
#1. #1. Given
#2. #2. Vertical angles congruent
#3. #3. Given
#4. #4. S.A.S.
(side-angle-side)
YWXVWZ
V
WZ
X
Y
WYVW YWXVWZ
XWZW
Prove
#1. #1. Given
#2. #2. Vertical angles congruent
#3. #3. Given
#4. #4. S.A.S.
(side-angle-side)
YWXVWZ
V
WZ
X
Y
WYVW YWXVWZ
XWZW
YWXVWZ
Prove
#1. #1. Given
#2. #2. Vertical angles congruent
#3. #3. Given
#4. #4. S.A.S.
(side-angle-side)
YWXVWZ
V
WZ
X
Y
WYVW YWXVWZ
XWZW
YWXVWZ
Prove
#1. #1. Given
#2. #2. Vertical angles congruent
#3. #3. Given
#4. #4. S.A.S.
(side-angle-side)
YWXVWZ
V
WZ
X
Y
WYVW YWXVWZ
XWZW
YWXVWZ
Can you prove
What do you need to show Congruent
NPMLMP
P
L M
N
Given:Prove:
#1. #1. Given
#2. , are #2. Def. of Prep. Lines
right angles
#3. #3. All Rt. Angles
#4. #4. Reflexive
#5. #5. S.A.S.
APMBPBAB ;
MBPMBA A B P
M
APMBPBAB ;
Given:Prove:
#1. #1. Given
#2. , are #2. Def. of Prep. Lines
right angles
#3. #3. All Rt. Angles
#4. #4. Reflexive
#5. #5. S.A.S.
APMBPBAB ;
MBPMBA A B P
M
APMBPBAB ;
ABM PBM
Given:Prove:
#1. #1. Given
#2. , are #2. Def. of Prep. Lines
right angles
#3. #3. All Rt. Angles
#4. #4. Reflexive
#5. #5. S.A.S.
APMBPBAB ;
MBPMBA A B P
M
APMBPBAB ;
ABM PBM
Given:Prove:
#1. #1. Given
#2. , are #2. Def. of Prep. Lines
right angles
#3. #3. All Rt. Angles
#4. #4. Reflexive
#5. #5. S.A.S.
APMBPBAB ;
MBPMBA A B P
M
APMBPBAB ;
ABM PBM
MBPABM
Given:Prove:
#1. #1. Given
#2. , are #2. Def. of Prep. Lines
right angles
#3. #3. All Rt. Angles
#4. #4. Reflexive
#5. #5. S.A.S.
APMBPBAB ;
MBPMBA A B P
M
APMBPBAB ;
ABM PBM
MBPABM
Given:Prove:
#1. #1. Given
#2. , are #2. Def. of Prep. Lines
right angles
#3. #3. All Rt. Angles
#4. #4. Reflexive
#5. #5. S.A.S.
APMBPBAB ;
MBPMBA A B P
M
APMBPBAB ;
ABM PBM
MBPABM
MBMB
Given:Prove:
#1. #1. Given
#2. , are #2. Def. of Prep. Lines
right angles
#3. #3. All Rt. Angles
#4. #4. Reflexive
#5. #5. S.A.S.
APMBPBAB ;
MBPMBA A B P
M
APMBPBAB ;
ABM PBM
MBPABM
MBMB
Given:Prove:
#1. #1. Given
#2. , are #2. Def. of Prep. Lines
right angles
#3. #3. All Rt. Angles
#4. #4. Reflexive
#5. #5. S.A.S.
APMBPBAB ;
MBPMBA A B P
M
APMBPBAB ;
MBPMBA
ABM PBM
MBPABM
MBMB
Given:Prove:
#1. #1. Given
#2. , are #2. Def. of Prep. Lines
right angles
#3. #3. All Rt. Angles
#4. #4. Reflexive
#5. #5. S.A.S.
APMBPBAB ;
MBPMBA A B P
M
APMBPBAB ;
MBPMBA
ABM PBM
MBPABM
MBMB
HomeworkHomework
Page 216 Page 216
##6 -17, 23, 266 -17, 23, 26
HomeworkHomework
Page 217- 219 Page 217- 219
## 18 – 22, 24, 18 – 22, 24,
25, 28, 34, 35, 25, 28, 34, 35,
41 – 43 41 – 43
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