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Notes 4.1-4.3 Triangle Congruence PowerPoint Presentation
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Notes 4.1-4.3 Triangle Congruence Learning Targets I can recognize congruent figures and their corresponding parts. I can prove triangles congruent using SSS and SAS. I can prove triangles congruent using ASA and AAS. Congruence.

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slide1

Notes 4.1-4.3 Triangle Congruence

Learning TargetsI can recognize congruentfigures and their corresponding parts. I can prove triangles congruent using SSS and SAS. I can prove triangles congruent using ASA and AAS.

slide2

Congruence

Two geometric figures with exactly the same size and shape.

slide3

Corresponding Parts

B

A

C

E

F

D

If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.

Example 1

  • AB DE
  • BC EF
  • AC DF
  •  A  D
  •  B  E
  •  C  F

ABC DEF

slide4

SSS

SAS

ASA

AAS

Do you need all six ?

NO !

slide6

Side-Side-Side (SSS)

B

A

C

E

F

  • Example 1
  • AB DE
  • BC EF
  • AC DF

D

ABC DEF

slide7

Included Angle

The angle between two sides

H

G

I

slide9

Side-Angle-Side (SAS)

B

E

F

A

C

D

  • AB DE
  • A D
  • AC DF

ABC DEF

included

angle

slide10

Included Side

The side between two angles

GI

GH

HI

slide11

E

Y

S

Included Side

Name the included side:

Y and E

E and S

S and Y

YE

ES

SY

slide13

Angle-Side-Angle (ASA)

B

E

F

A

C

D

  • A D
  • AB  DE
  • B E

ABC DEF

included

side

slide15

Angle-Angle-Side (AAS)

B

E

F

A

C

D

  • A D
  • B E
  • BC  EF

ABC DEF

Non-included

side

slide16

Warning: No SSA Postulate

There is no such thing as an SSA postulate!

E

B

F

A

C

D

NOT CONGRUENT

slide17

Warning: No AAA Postulate

There is no such thing as an AAA postulate!

E

B

A

C

F

D

NOT CONGRUENT

slide18

SSS

  • ASA
  • SAS
  • AAS
  • SSA
  • AAA

The Congruence Postulates

slide19

Name That Postulate

(when possible)

SAS

ASA

SSA

SSS

slide20

Name That Postulate

(when possible)

AAA

ASA

SSA

SAS

slide21

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: