4.4 & 4.5 Proving Triangles

Congruent

4.4 & 4.5 Proving Triangles

Congruent

Interactive notebook Entries

• Pg. 17 4-4 & 4-5: Proving Triangles Congruent

• Pg. 18 Proving Triangles Congruent (Practice)

Objectives:• Use the SSS, SAS, ASA, AAS

and HL postulates to test for triangle congruence.

In Lesson 4.3, 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 !

SSSSASASAAASHL

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

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

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

Hypotenuse-Leg (HL)Hypotenuse-Leg (HL)

1. AC ZX2. BC YX

B C

A

X

Z

Y

ABC ZYX

RIGHT TRIANGLES

Warning:Warning: No SSA Postulate No SSA Postulate

A C

B

D

E

F

NOT ALWAYS 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!

NOT ALWAYS CONGRUENT

The Congruence PostulatesThe Congruence Postulates

SSS correspondence

ASA correspondence

SAS correspondence

AAS correspondence

HL 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