Ch 5. Proving Triangles Congruent

(Sec 5.4 – Sec 5.6)

Ch 5. Proving Triangles Congruent

(Sec 5.4 – Sec 5.6)

Objectives: What we’ll learn…

• Identify corresponding parts of congruent triangles.

• Use SSS and SAS tests for congruence.

• Use ASA and AAS tests for congruence.

Two geometric figures with exactly the same shape and size.

The Idea of a CongruenceThe Idea of a Congruence

A C

B

DE

FNOT Congruent!!!

B

A C

E

D

F

Yes, they are Congruent.

Why Congruence?When factory manufactures cars, each car must be identical (congruent)……

If not congruent = defects= Company losing $$$$$$

Why triangles?

• It’s a simple polygon!!!

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

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

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

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

NO !

SSSSASASAAAS

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

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

The angle between two sides

Included AngleIncluded Angle

G I H

Name the included angle:

YE and ES

ES and YS

YS and YE

Included AngleIncluded Angle

SY

E

E

S

Y

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

The side between two angles

Included SideIncluded Side

GI HI GH

Name the included side:

Y and E

E and S

S and Y

Included SideIncluded Side

SY

E

YE

ES

SY

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

Warning:Warning: No SSA Postulate No SSA Postulate

TRIANGLES NOT CONGRUENT

There is no such thing as an SSA

postulate!

Warning:Warning: No AAA Postulate No AAA Postulate

A C

B

D

E

F

There is no such thing as an AAA

postulate!

All congruent angles, but NOT congruent in size.

The Congruence PostulatesThe Congruence Postulates

SSS correspondence

ASA correspondence

SAS correspondence

AAS correspondence

SSA correspondence

AAA correspondence

Name That PostulateName That Postulate

SASSASASAASA

SSSSSSSSASSA

(when possible)

Name That PostulateName That Postulate(when possible)

ASAASA

SASASS

AAAAAA

SSASSA

Name That PostulateName That Postulate(when possible)

SASASS

SASSAS

SASASS

Reflexive Property

Vertical Angles

Vertical Angles

Reflexive Property SSSS

AA

HW: Name That PostulateHW: Name That Postulate(when possible)

(when possible)HW: Name That PostulateHW: Name That Postulate

Included Angle

Included Side

Hexagon vs. Pentagon

Hint: No AAA Postulate

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

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

For ASA:

For SAS:

For AAS:

This powerpoint was kindly donated to www.worldofteaching.com

http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.