4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.
-
Upload
alexandrina-daniel -
Category
Documents
-
view
264 -
download
4
Transcript of 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.
![Page 1: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/1.jpg)
4.3 Proving Triangles are 4.3 Proving Triangles are Congruent Congruent
Side-Side-SideSide-Side-Side
Side-Angle-SideSide-Angle-Side
![Page 2: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/2.jpg)
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
![Page 3: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/3.jpg)
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
![Page 4: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/4.jpg)
Name the congruent Triangles
K
M PL
N
![Page 5: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/5.jpg)
Name the congruent Triangles
K
M PL
N
NMPKLM
![Page 6: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/6.jpg)
Prove YWXVWZ
V
WZ
X
Y
![Page 7: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/7.jpg)
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
![Page 8: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/8.jpg)
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
![Page 9: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/9.jpg)
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
![Page 10: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/10.jpg)
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
![Page 11: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/11.jpg)
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
![Page 12: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/12.jpg)
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
![Page 13: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/13.jpg)
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
![Page 14: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/14.jpg)
Can you prove
What do you need to show Congruent
NPMLMP
P
L M
N
![Page 15: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/15.jpg)
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 ;
![Page 16: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/16.jpg)
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
![Page 17: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/17.jpg)
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
![Page 18: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/18.jpg)
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
![Page 19: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/19.jpg)
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
![Page 20: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/20.jpg)
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
![Page 21: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/21.jpg)
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
![Page 22: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/22.jpg)
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
![Page 23: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/23.jpg)
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
![Page 24: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/24.jpg)
HomeworkHomework
Page 216 Page 216
##6 -17, 23, 266 -17, 23, 26
![Page 25: 4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.](https://reader035.fdocuments.net/reader035/viewer/2022081418/56649db95503460f94aa8dd5/html5/thumbnails/25.jpg)
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