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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
slide2

How much do you

need to know. . .

. . . about two triangles

to prove that they

are congruent?

slide3

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

slide4

SSS

SAS

ASA

AAS

Do you need all six ?

NO !

slide5

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

slide6

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

slide7

Included Angle

The angle between two sides

H

G

I

slide8

E

Y

S

Included Angle

Name the included angle:

YE and ES

ES and YS

YS and YE

E

S

Y

slide9

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.

slide10

Included Side

The side between two angles

GI

GH

HI

slide11

E

Y

S

Included Side

Name the included angle:

Y and E

E and S

S and Y

YE

ES

SY

slide12

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

slide13

Warning: No SSA Postulate

There is no such thing as an SSA postulate!

E

B

F

A

C

D

NOT CONGRUENT

slide14

Warning: No AAA Postulate

There is no such thing as an AAA postulate!

E

B

A

C

F

D

NOT CONGRUENT

slide15

Name That Postulate

(when possible)

SAS

ASA

SSA

SSS

slide16

Name That Postulate

(when possible)

AAA

ASA

SSA

SAS

slide17

Name That Postulate

(when possible)

Vertical Angles

Reflexive Property

SAS

SAS

Reflexive Property

Vertical Angles

SSA

SAS

slide18

Name That Postulate

(when possible)

slide20

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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