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Proving Triangles Congruent

Proving Triangles Congruent

Free powerpoints at http://www.worldofteaching.com

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Two geometric figures with exactly the same size and shape.

The Idea of a CongruenceThe Idea of a Congruence

A C

B

DE

F

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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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In Lesson 4.2, 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 angle:

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

A C

B

D

E

F

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!

NOT CONGRUENT

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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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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: