proving triangles congruent

Proving Triangles Congruent

Proving Triangles Congruent

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Two TRIANGLES with exactly the same size and shape.

Congruent Triangles

A C

B

DE

F

How much do you need to know. . .

. . . about two triangles to prove that they are congruent?

Corresponding Parts

ABC DEF

B

A

C

E

D

F

1. AB DE

2. BC EF

3. AC DF

4. A D5. B E6. C F

Do you need all six ?

NO !

SSSSASASAAAS

Side-Side-Side (SSS)

1. AB DE

2. BC EF

3. AC DF

ABC DEF

B

A

C

E

D

F

Side-Angle-Side (SAS)

1. AB DE

2. A D

3. AC DF

ABC DEF

B

A

C

E

D

F

included angle

The angle between two sides

Included Angle

G I H

Name the included angle:

YE and ES

ES and YS

YS and YE

Included Angle

SY

E

E

S

Y

Angle-Side-Angle (ASA)

1. A D2. AB DE

3. B E

ABC DEF

B

A

C

E

D

F

Included

side

The side between two angles

Included Side

GI HI GH

Name the included side:

Y and E

E and S

S and Y

Included Side

SY

E

YE

ES

SY

Angle-Angle-Side (AAS)

1. A D

2. B E

3. BC EF

ABC DEF

B

A

C

E

D

F

Non-included

side

Warning: No SSA Postulate

A C

B

D

E

F

NOT CONGRUENT

There is no such thing as an SSA

postulate!

Warning: No AAA Postulate

A C

B

D

E

F

There is no such thing as an AAA

postulate!

NOT CONGRUENT

The Congruence Postulates

SSS correspondence

ASA correspondence

SAS correspondence

AAS correspondence

SSA correspondence

AAA correspondence

Name That Postulate

SASASA

SSSSSA

(when possible)

1.2.

3.4.

Name That Postulate(when possible)

ASA

SAS

AAA

SSA

5.6.

7.8.

Name That Postulate(when possible)

SAS

SAS

SAS

Reflexive Property

Vertical Angles

Vertical Angles

Reflexive Property SS

A

9.10.

11. 12.

HW: Name That Postulate(when possible)

13.14.

15.16.

(when possible)HW: Name That Postulate

17.18.

19.

Let’s PracticeIndicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

For SAS:

B D

For AAS: A F

AC FE

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

For ASA:

For SAS:

For AAS:

20.

21.

22.