Transcript Document
Proving Triangles Congruent
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The Idea of a Congruence
Two geometric figures with exactly the same size and shape.
F B A C E D
How much do you need to know. . .
. . . about two triangles to prove that they are congruent?
Corresponding Parts In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.
1. AB
2. BC
3. AC
4.
5.
6.
A B C
DE EF DF
D E F
ABC
DEF
Do you need all six ? NO !
SSS SAS ASA AAS
Side-Side-Side (SSS) 1. AB
2. BC
3. AC
DE EF DF
ABC
DEF
Side-Angle-Side (SAS) 1. AB
2.
A
3. AC
DE
D DF
ABC
DEF included angle
Included Angle
The angle between two sides G I H
Y S E
Included Angle
Name the included angle: Y E and E S E S and Y S Y S and Y E E S Y
Angle-Side Angle (ASA) 1.
A
2. AB
3.
B
DE D
E
ABC
DEF included side
Included Side
The side between two angles
GI HI GH
Y S E
Included Side
Name the included side: Y and E E and S S and Y
YE ES SY
Angle-Angle-Side (AAS) 1.
2.
A
B
3. BC
D
E EF
ABC
DEF Non-included side
Warning:
No SSA Postulate
There is no such thing as an SSA postulate!
B E A C D
NOT CONGRUENT
F
Warning:
No AAA Postulate
There is no such thing as an AAA postulate!
B A E C D
NOT CONGRUENT
F
The Congruence Postulates SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence
Name That Postulate (when possible)
SAS ASA SSA SSS
Name That Postulate (when possible)
AAA ASA SAS SSA
Name That Postulate (when possible) Reflexive Property
SAS
Vertical Angles
SAS
Vertical Angles
SAS
Reflexive Property
SSA
HW: Name That Postulate (when possible)
HW: Name That Postulate (when possible)
Let’s Practice Indicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA: For SAS: For AAS:
B
AC
A
D FE
F
HW Indicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA: For SAS: For AAS: