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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

Proving Triangles Congruent

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

slide2

F

B

A

C

E

D

The Idea of a Congruence

Two geometric figures with exactly the same size and shape.

slide3

How much do you

need to know. . .

. . . about two triangles

to prove that they

are congruent?

slide4

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

slide5

SSS

SAS

ASA

AAS

Do you need all six ?

NO !

slide6

Side-Side-Side (SSS)

E

B

F

A

D

C

  • AB DE
  • BC EF
  • AC DF

ABC DEF

slide7

Side-Angle-Side (SAS)

B

E

F

A

C

D

  • AB DE
  • A D
  • AC DF

ABC DEF

included

angle

slide8

Included Angle

The angle between two sides

H

G

I

slide9

E

Y

S

Included Angle

Name the included angle:

YE and ES

ES and YS

YS and YE

E

S

Y

slide10

Angle-Side-Angle (ASA)

B

E

F

A

C

D

  • A D
  • AB  DE
  • B E

ABC DEF

included

side

slide11

Included Side

The side between two angles

GI

GH

HI

slide12

E

Y

S

Included Side

Name the included side:

Y and E

E and S

S and Y

YE

ES

SY

slide13

Angle-Angle-Side (AAS)

B

E

F

A

C

D

  • A D
  • B E
  • BC  EF

ABC DEF

Non-included

side

slide14

Warning: No SSA Postulate

There is no such thing as an SSA postulate!

E

B

F

A

C

D

NOT CONGRUENT

slide15

Warning: No AAA Postulate

There is no such thing as an AAA postulate!

E

B

A

C

F

D

NOT CONGRUENT

slide16

SSS correspondence

  • ASA correspondence
  • SAS correspondence
  • AAS correspondence
  • SSA correspondence
  • AAA correspondence

The Congruence Postulates

slide17

Name That Postulate

(when possible)

SAS

ASA

SSA

SSS

slide18

Name That Postulate

(when possible)

AAA

ASA

SSA

SAS

slide19

Name That Postulate

(when possible)

Vertical Angles

Reflexive Property

SAS

SAS

Reflexive Property

Vertical Angles

SSA

SAS

slide22

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:

slide23

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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