Proving triangles congruent
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Proving Triangles Congruent. How much do you need to know. . . . . . about two triangles to prove that they are congruent?. Corresponding Parts. AB  DE BC  EF AC  DF  A   D  B   E  C   F. B. A. C. E. F. D.

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Presentation Transcript

How much do you

need to know. . .

. . . about two triangles

to prove that they

are congruent?


Corresponding Parts

  • AB DE

  • BC EF

  • AC DF

  •  A  D

  •  B  E

  •  C  F

B

A

C

E

F

D

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

ABC DEF


SSS

SAS

ASA

AAS

Do you need all six ?

NO !


Side-Side-Side (SSS)

E

B

F

A

D

C

  • AB DE

  • BC EF

  • AC DF

ABC DEF

If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent


Side-Angle-Side (SAS)

B

E

F

A

C

D

  • AB DE

  • A D

  • AC DF

ABC DEF

included

angle

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent


Included Angle

The angle between two sides

H

G

I


E

Y

S

Included Angle

Name the included angle:

YE and ES

ES and YS

YS and YE

E

S

Y


Angle-Side-Angle (ASA)

B

E

F

A

C

D

  • A D

  • AB  DE

  • B E

ABC DEF

included

side

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.


Included Side

The side between two angles

GI

GH

HI


E

Y

S

Included Side

Name the included angle:

Y and E

E and S

S and Y

YE

ES

SY


Angle-Angle-Side (AAS)

B

E

F

A

C

D

  • A D

  • B E

  • BC  EF

ABC DEF

Non-included

side

If 2 angles and a non-included side of 1 triangle are congruent to 2 angles and the corresponding non-included side of another triangle, then the 2 triangles are congruent


Warning: No SSA Postulate

There is no such thing as an SSA postulate!

E

B

F

A

C

D

NOT CONGRUENT


Warning: No AAA Postulate

There is no such thing as an AAA postulate!

E

B

A

C

F

D

NOT CONGRUENT


Name That Postulate

(when possible)

SAS

ASA

SSA

SSS


Name That Postulate

(when possible)

AAA

ASA

SSA

SAS


Name That Postulate

(when possible)

Vertical Angles

Reflexive Property

SAS

SAS

Reflexive Property

Vertical Angles

SSA

SAS


Name That Postulate

(when possible)


HW: Name That Postulate

(when possible)


Let’s Practice

ACFE

Indicate the additional information needed to enable us to prove the triangles are congruent.

For ASA: B D

For SAS:

AF

For AAS:


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