Proving Triangles Congruent
Proving Triangles Congruent
jc-schools.net/PPT/geometrycongruence.ppt
Two geometric figures with exactly the same size and shape.
The Idea of a CongruenceThe Idea of a Congruence
A C
B
DE
F
jc-schools.net/PPT/geometrycongruence.ppt
How much do you How much do you need to know. . .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)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)Side-Side-Side (SSS)
1. AB DE
2. BC EF
3. AC DF
ABC DEF
B
A
C
E
D
F
jc-schools.net/PPT/geometrycongruence.ppt
Side-Angle-Side (SAS)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)Side-Angle-Side (SAS)
1. AB DE
2. A D
3. AC DF
ABC DEF
B
A
C
E
D
F
included angle
jc-schools.net/PPT/geometrycongruence.ppt
The angle between two sides
Included AngleIncluded Angle
G I H
jc-schools.net/PPT/geometrycongruence.ppt
Name the included angle:
YE and ES
ES and YS
YS and YE
Included AngleIncluded Angle
SY
E
E
S
Y
jc-schools.net/PPT/geometrycongruence.ppt
The side between two angles
Included SideIncluded Side
GI HI GH
jc-schools.net/PPT/geometrycongruence.ppt
Name the included side:
Y and E
E and S
S and Y
Included SideIncluded Side
SY
E
YE
ES
SY
jc-schools.net/PPT/geometrycongruence.ppt
How are the triangles congruent?How are the triangles congruent?
SASASS
SASSAS
SASASS
Reflexive Property
Vertical Angles
Vertical Angles
jc-schools.net/PPT/geometrycongruence.ppt
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