Proving triangles congruent
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Proving Triangles Congruent. Free powerpoints at http://www.worldofteaching.com. F. B. A. C. E. D. The Idea of a Congruence. Two geometric figures with exactly the same size and shape. How much do you need to know. . . . . . about two triangles

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Proving Triangles Congruent

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Proving triangles congruent

Proving Triangles Congruent

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


Proving triangles congruent

F

B

A

C

E

D

The Idea of a Congruence

Two geometric figures with exactly the same size and shape.


Proving triangles congruent

How much do you

need to know. . .

. . . about two triangles

to prove that they

are congruent?


Proving triangles congruent

Corresponding Parts

  • AB DE

  • BC EF

  • AC DF

  •  A  D

  •  B  E

  •  C  F

B

A

C

E

F

D

In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.

ABC DEF


Proving triangles congruent

SSS

SAS

ASA

AAS

Do you need all six ?

NO !


Proving triangles congruent

Side-Side-Side (SSS)

E

B

F

A

D

C

  • AB DE

  • BC EF

  • AC DF

ABC DEF


Proving triangles congruent

Side-Angle-Side (SAS)

B

E

F

A

C

D

  • AB DE

  • A D

  • AC DF

ABC DEF

included

angle


Proving triangles congruent

Included Angle

The angle between two sides

H

G

I


Proving triangles congruent

E

Y

S

Included Angle

Name the included angle:

YE and ES

ES and YS

YS and YE

E

S

Y


Proving triangles congruent

Angle-Side-Angle (ASA)

B

E

F

A

C

D

  • A D

  • AB  DE

  • B E

ABC DEF

included

side


Proving triangles congruent

Included Side

The side between two angles

GI

GH

HI


Proving triangles congruent

E

Y

S

Included Side

Name the included side:

Y and E

E and S

S and Y

YE

ES

SY


Proving triangles congruent

Angle-Angle-Side (AAS)

B

E

F

A

C

D

  • A D

  • B E

  • BC  EF

ABC DEF

Non-included

side


Proving triangles congruent

Warning: No SSA Postulate

There is no such thing as an SSA postulate!

E

B

F

A

C

D

NOT CONGRUENT


Proving triangles congruent

Warning: No AAA Postulate

There is no such thing as an AAA postulate!

E

B

A

C

F

D

NOT CONGRUENT


Proving triangles congruent

  • SSS correspondence

  • ASA correspondence

  • SAS correspondence

  • AAS correspondence

  • SSA correspondence

  • AAA correspondence

The Congruence Postulates


Proving triangles congruent

Name That Postulate

(when possible)

SAS

ASA

SSA

SSS


Proving triangles congruent

Name That Postulate

(when possible)

AAA

ASA

SSA

SAS


Proving triangles congruent

Name That Postulate

(when possible)

Vertical Angles

Reflexive Property

SAS

SAS

Reflexive Property

Vertical Angles

SSA

SAS


Proving triangles congruent

HW: Name That Postulate

(when possible)


Proving triangles congruent

HW: Name That Postulate

(when possible)


Proving triangles congruent

Let’s Practice

ACFE

Indicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

B D

For SAS:

AF

For AAS:


Proving triangles congruent

HW

Indicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

For SAS:

For AAS:


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