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Proving Triangles Congruent Sss, Sas Asa

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Page 1: Proving Triangles Congruent Sss, Sas Asa

Proving Triangles Congruent

Proving Triangles Congruent

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

Page 2: Proving Triangles Congruent Sss, Sas Asa

Two geometric figures with exactly the same size and shape.

The Idea of a CongruenceThe Idea of a Congruence

A C

B

DE

F

Page 3: Proving Triangles Congruent Sss, Sas Asa

How much do you How much do you need to know. . .need to know. . .

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

Page 4: Proving Triangles Congruent Sss, Sas Asa

In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.

Corresponding PartsCorresponding Parts

ABC DEF

B

A C

E

D

F

1. AB DE

2. BC EF

3. AC DF

4. A D

5. B E

6. C F

Page 5: Proving Triangles Congruent Sss, Sas Asa

Do you need Do you need all six ?all six ?

NO !

Page 6: Proving Triangles Congruent Sss, Sas Asa

Side-Side-Side (SSS)Side-Side-Side (SSS)

1. AB DE

2. BC EF

3. AC DF

ABC DEF

B

A

C

E

D

F

Page 7: Proving Triangles Congruent Sss, Sas Asa

Side-Angle-Side (SAS)Side-Angle-Side (SAS)

1. AB DE

2. A D

3. AC DF

ABC DEF

B

A

C

E

D

F

included angle

Page 8: Proving Triangles Congruent Sss, Sas Asa

The angle between two sides

Included AngleIncluded Angle

G I H

Page 9: Proving Triangles Congruent Sss, Sas Asa

Name the included angle:

YE and ES

ES and YS

YS and YE

Included AngleIncluded Angle

SY

E

E

S

Y

Page 10: Proving Triangles Congruent Sss, Sas Asa

Angle-Side-Angle-Side-AngleAngle (ASA) (ASA)

1. A D

2. AB DE

3. B E

ABC DEF

B

A

C

E

D

F

included side

Page 11: Proving Triangles Congruent Sss, Sas Asa

The side between two angles

Included SideIncluded Side

GI HI GH

Page 12: Proving Triangles Congruent Sss, Sas Asa

Name the included side:

Y and E

E and S

S and Y

Included SideIncluded Side

SY

E

YE

ES

SY

Page 13: Proving Triangles Congruent Sss, Sas Asa

Angle-Angle-Side (AAS)Angle-Angle-Side (AAS)

1. A D

2. B E

3. BC EF

ABC DEF

B

A

C

E

D

F

Non-included

side

Page 14: Proving Triangles Congruent Sss, Sas Asa

Warning:Warning: No SSA Postulate No SSA Postulate

A C

B

D

E

F

NOT CONGRUENT

There is no such thing as an SSA

postulate!

Page 15: Proving Triangles Congruent Sss, Sas Asa

Warning:Warning: No AAA Postulate No AAA Postulate

A C

B

D

E

F

There is no such thing as an AAA

postulate!

NOT CONGRUENT

Page 16: Proving Triangles Congruent Sss, Sas Asa

The Congruence PostulatesThe Congruence Postulates

SSS correspondence

ASA correspondence

SAS correspondence

AAS correspondence

SSA correspondence

AAA correspondence

Page 17: Proving Triangles Congruent Sss, Sas Asa

Name That PostulateName That Postulate

SASSASASAASA

SSSSSSSSASSA

(when possible)

Page 18: Proving Triangles Congruent Sss, Sas Asa

Name That PostulateName That Postulate(when possible)

ASAASA

SASASS

AAAAAA

SSASSA

Page 19: Proving Triangles Congruent Sss, Sas Asa

Name That PostulateName That Postulate(when possible)

SASASS

SASSAS

SASASS

Reflexive Property

Vertical Angles

Vertical Angles

Reflexive Property SSSS

AA

Page 20: Proving Triangles Congruent Sss, Sas Asa

Name That PostulateName That Postulate(when possible)

Page 21: Proving Triangles Congruent Sss, Sas Asa

(when possible)Name That PostulateName That Postulate

Page 22: Proving Triangles Congruent Sss, Sas Asa

Let’s PracticeLet’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

Page 23: Proving Triangles Congruent Sss, Sas Asa

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

For ASA:

For SAS:

For AAS:

Page 24: Proving Triangles Congruent Sss, Sas Asa

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

ΔGIH ΔJIK by AAS

G

I

H J

KEx 4

Page 25: Proving Triangles Congruent Sss, Sas Asa

ΔABC ΔEDC by ASA

B A

C

ED

Ex 5

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

Page 26: Proving Triangles Congruent Sss, Sas Asa

ΔACB ΔECD by SASB

A

C

E

D

Ex 6

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

Page 27: Proving Triangles Congruent Sss, Sas Asa

ΔJMK ΔLKM by SAS or ASA

J K

LM

Ex 7

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

Page 28: Proving Triangles Congruent Sss, Sas Asa

Not possible

K

J

L

T

U

Ex 8

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

V

Page 29: Proving Triangles Congruent Sss, Sas Asa

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