proving triangles congruent
DESCRIPTION
Proving Triangles Congruent. Part 2. AAS Theorem. If two angles and one of the non-included sides in one triangle are congruent to two angles and one of the non-included sides in another triangle, then the triangles are congruent. AAS Looks Like…. A. G. F. A: Ð K @ Ð M - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/1.jpg)
Proving Triangles Congruent
Part 2
![Page 2: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/2.jpg)
AAS Theorem
If two angles and one of the non-included sides in one triangle are congruent to two angles and one
of the non-included sides in another triangle, then the triangles
are congruent.
![Page 3: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/3.jpg)
AAS Looks Like…
B C D
FGA
ACB DFG
A: A DA: B GS: AC DF
J
K LM
A: K MA: KJL MJLS: JL JLJKL JML
![Page 4: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/4.jpg)
AAS vs. ASA
ASAAAS
![Page 5: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/5.jpg)
Parts of a Right Triangle
legs
hypotenuse
![Page 6: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/6.jpg)
HL TheoremRIGHT TRIANGLES ONLY!
If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.
![Page 7: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/7.jpg)
HL Looks Like…
XTV
W
WTV WXV
NMP RQS
NM
P
SQ
R
Right : M & QH: PN RSL: MP QS
Right : TVW &
XVW
H: TW XW
L: WV WV
![Page 8: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/8.jpg)
There’s no such thing as AAAAAA Congruence:
These two equiangular triangles have all the same angles… but they are not the same size!
![Page 9: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/9.jpg)
Recap:
There are 5 ways to prove that triangles are congruent:
SSS
SAS
ASA
AAS
HL
![Page 10: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/10.jpg)
Examples
A B C
D
B is the midpoint of AC
SAS ABD CBDK
J
LN
M
H
AAS
MLN HJK
S: AB BCA: ABD CBDS: DB DB
A:L JA: M HS: LN JK
![Page 11: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/11.jpg)
Right Angles: ABD & CBDH: AD CDL: BD BD
Examples C
DA
B
E
B C
D
A
DB AC AD CD
HL
ABD CBDA: A CS: AE CEA: BEA DEC
ASA
BEA DEC
![Page 12: Proving Triangles Congruent](https://reader030.vdocuments.us/reader030/viewer/2022032709/56813051550346895d960196/html5/thumbnails/12.jpg)
Examples
B C
D
A
B is the midpoint of AC
SSS
DAB DCB
Z
Y
X
V
W
Not Enough!
We cannot conclude whether the triangle are
congruent.
S: AB CBS: BD BDS: AD CD
A: WXV YXZS: WV YZ