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)
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Ch 5. Proving Triangles Congruent
(Sec 5.4 – Sec 5.6)
Ch 5. Proving Triangles Congruent
(Sec 5.4 – Sec 5.6)
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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.
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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.
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Why Congruence?When factory manufactures cars, each car must be identical (congruent)……
If not congruent = defects= Company losing $$$$$$
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Why triangles?
• It’s a simple polygon!!!
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How much do you How much do you need to know. . .need to know. . .
. . . about two triangles to prove that they are congruent?
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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
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Do you need Do you need all six ?all six ?
NO !
SSSSASASAAAS
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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
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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
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The angle between two sides
Included AngleIncluded Angle
G I H
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Name the included angle:
YE and ES
ES and YS
YS and YE
Included AngleIncluded Angle
SY
E
E
S
Y
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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
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The side between two angles
Included SideIncluded Side
GI HI GH
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Name the included side:
Y and E
E and S
S and Y
Included SideIncluded Side
SY
E
YE
ES
SY
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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
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Warning:Warning: No SSA Postulate No SSA Postulate
TRIANGLES NOT CONGRUENT
There is no such thing as an SSA
postulate!
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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.
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The Congruence PostulatesThe Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
SSA correspondence
AAA correspondence
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Name That PostulateName That Postulate
SASSASASAASA
SSSSSSSSASSA
(when possible)
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Name That PostulateName That Postulate(when possible)
ASAASA
SASASS
AAAAAA
SSASSA
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Name That PostulateName That Postulate(when possible)
SASASS
SASSAS
SASASS
Reflexive Property
Vertical Angles
Vertical Angles
Reflexive Property SSSS
AA
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HW: Name That PostulateHW: Name That Postulate(when possible)
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(when possible)HW: Name That PostulateHW: Name That Postulate
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Included Angle
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Included Side
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Hexagon vs. Pentagon
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Hint: No AAA Postulate
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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
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HWHWIndicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
For AAS:
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