Transcript Document

Proving Triangles
Congruent
jc-schools.net/PPT/geometrycongruence.ppt
The Idea of a Congruence
Two geometric figures with
exactly the same size and
shape.
F
B
A
C
jc-schools.net/PPT/geometrycongruence.ppt
E
D
How much do you
need to know. . .
. . . about two triangles
to prove that they
are congruent?
jc-schools.net/PPT/geometrycongruence.ppt
Reflexive Property of
Congruence
• A segment is congruent to itself.
• An angle is congruent to itself.
Side-Side-Side (SSS)
Postulate 8-1:
If three sides of one triangle
are congruent to three sides of
another triangle, then the two
triangles are congruent.
Side-Side-Side (SSS)
1. AB  DE
2. BC  EF
ABC   DEF
3. AC  DF
jc-schools.net/PPT/geometrycongruence.ppt
Side-Angle-Side (SAS)
Postulate 8-2:
If two sides and the included
angle of one triangle are
congruent to two sides and the
included angle of another
triangle, then the two triangles
are congruent.
Side-Angle-Side (SAS)
1. AB  DE
2. A   D
3. AC  DF
ABC   DEF
included
angle
jc-schools.net/PPT/geometrycongruence.ppt
Included Angle
The angle between two sides
G
I
jc-schools.net/PPT/geometrycongruence.ppt
H
Included Angle
Name the included angle:
E
Y
S
YE and ES
E
ES and YS
S
YS and YE
Y
jc-schools.net/PPT/geometrycongruence.ppt
Included Side
The side between two angles
GI
HI
jc-schools.net/PPT/geometrycongruence.ppt
GH
Included Side
Name the included angle:
E
Y
S
Y and E
YE
E and S
ES
S and Y
SY
jc-schools.net/PPT/geometrycongruence.ppt
How are the triangles congruent?
Reflexive
Property
SAS
Vertical
Angles
SAS
jc-schools.net/PPT/geometrycongruence.ppt
Vertical
Angles
SAS
Homework
Work Packet: SSS and SAS