Ch 5. Proving Triangles Congruent (Sec 5.4 – Sec 5.6)
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Transcript of Ch 5. Proving Triangles Congruent (Sec 5.4 – Sec 5.6)
Ch 5. Proving Triangles Congruent
(Sec 5.4 – Sec 5.6)
Ch 5. Proving Triangles Congruent
(Sec 5.4 – Sec 5.6)
Objectives: What we’ll learn…
• Identify corresponding parts of congruent triangles.
• Use SSS and SAS tests for congruence.
• Use ASA and AAS tests for congruence.
Two geometric figures with exactly the same shape and size.
The Idea of a CongruenceThe Idea of a Congruence
A C
B
DE
FNOT Congruent!!!
B
A C
E
D
F
Yes, they are Congruent.
Why Congruence?When factory manufactures cars, each car must be identical (congruent)……
If not congruent = defects= Company losing $$$$$$
Why triangles?
• It’s a simple polygon!!!
How much do you How much do you need to know. . .need to know. . .
. . . about two triangles to prove that they are congruent?
You learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.
Corresponding PartsCorresponding Parts
ABC DEF
B
A C
E
D
F
1. AB DE
2. BC EF
3. AC DF
4. A D
5. B E
6. C F
Do you need Do you need all six ?all six ?
NO !
SSSSASASAAAS
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
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
The angle between two sides
Included AngleIncluded Angle
G I H
Name the included angle:
YE and ES
ES and YS
YS and YE
Included AngleIncluded Angle
SY
E
E
S
Y
Angle-Side-Angle-Side-AngleAngle (ASA) (ASA)
1. A D
2. AB DE
3. B E
ABC DEF
B
A
C
E
D
F
included
side
The side between two angles
Included SideIncluded Side
GI HI GH
Name the included side:
Y and E
E and S
S and Y
Included SideIncluded Side
SY
E
YE
ES
SY
Angle-Angle-Side (AAS)Angle-Angle-Side (AAS)
1. A D
2. B E
3. BC EF
ABC DEF
B
A
C
E
D
F
Non-included
side
Warning:Warning: No SSA Postulate No SSA Postulate
TRIANGLES NOT CONGRUENT
There is no such thing as an SSA
postulate!
Warning:Warning: No AAA Postulate No AAA Postulate
A C
B
D
E
F
There is no such thing as an AAA
postulate!
All congruent angles, but NOT congruent in size.
The Congruence PostulatesThe Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
SSA correspondence
AAA correspondence
Name That PostulateName That Postulate
SASSASASAASA
SSSSSSSSASSA
(when possible)
Name That PostulateName That Postulate(when possible)
ASAASA
SASASS
AAAAAA
SSASSA
Name That PostulateName That Postulate(when possible)
SASASS
SASSAS
SASASS
Reflexive Property
Vertical Angles
Vertical Angles
Reflexive Property SSSS
AA
HW: Name That PostulateHW: Name That Postulate(when possible)
(when possible)HW: Name That PostulateHW: Name That Postulate
Included Angle
Included Side
Hexagon vs. Pentagon
Hint: No AAA Postulate
Let’s PracticeLet’s PracticeIndicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
B D
For AAS: A F
AC FE
HWHWIndicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
For AAS:
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