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Honors Geometry 14 Nov 2011. Take papers from your folder and put them in your binder. Place your binder, HW and text on your desk. YOUR FOLDERS SHOULD BE EMPTY EXCEPT FOR YOUR WARM UP PAPER and current day’s classwork Warm-up- silently please  1)read page 232.

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Honors Geometry 14 Nov 2011

EXCEPT FOR YOUR WARM UP PAPER and current day’s classwork

what does CPCTC mean?

2)do pg. 230, # 11

Students will review congruency shortcuts and use CPCTC to prove congruency

Students will view a powerpoint presentation, take notes and work independently and with their group to solve problems.

none

Homework due Nov. 15

P1- extension-pg. 224: 1-21 odds

Pg. 229: 2 – 20 evens

TEST- Nov 16/17

Study: constructions, isosceles triangle properties, triangle sum, triangle inequalities, triangle congruency shortcuts

### Proving Triangles Congruent

B

A

C

E

D

The Idea of a Congruence

Two geometric figures with exactly the same size and shape.

need to know. . .

. . . about two triangles

to prove that they

are congruent?

• AB DE

• BC EF

• AC DF

•  A  D

•  B  E

•  C  F

B

A

C

E

F

D

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

ABC DEF

SAS

ASA

AAS

Do you need all six ?

NO !

E

B

F

A

D

C

• AB DE

• BC EF

• AC DF

ABC DEF

B

E

F

A

C

D

• AB DE

• A D

• AC DF

ABC DEF

included

angle

The angle between two sides

H

G

I

Y

S

Included Angle

Name the included angle:

YE and ES

ES and YS

YS and YE

E

S

Y

Angle-Side-Angle (ASA)

B

E

F

A

C

D

• A D

• AB  DE

• B E

ABC DEF

included

side

The side between two angles

GI

GH

HI

Y

S

Included Side

Name the includedside:

Y and E

E and S

S and Y

YE

ES

SY

B

E

F

A

C

D

• A D

• B E

• BC  EF

ABC DEF

Non-included

side

Warning: No SSA Postulate

There is no such thing as an SSA postulate!

E

B

F

A

C

D

NOT necessarily CONGRUENT

Warning: No AAA Postulate

There is no such thing as an AAA postulate!

E

B

A

C

F

D

NOT necessarily CONGRUENT

• SSS correspondence

• ASA correspondence

• SAS correspondence

• AAS correspondence

• SSA correspondence

• AAA correspondence

The Congruence Postulates

(when possible)

SAS

ASA

SSA

SSS

(when possible)

AAA

ASA

SSA

SAS

(when possible)

take notes…

Vertical Angles

Reflexive Property

SAS

SAS

Reflexive Property

Vertical Angles

SSA

SAS

CW: Name That Postulate

(when possible)

CW: Name That Postulate

(when possible)

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:

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

For ASA:

For SAS:

For AAS:

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F

That means that EG CB

A

E

What is AC congruent to?

FE

G

C

Corresponding parts

When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are ,

that means that ALL the corresponding parts are congruent.

EX: If a triangle is congruent by ASA (for instance), then all the other corresponding parts are .

Corresponding parts of congruent triangles are congruent.

Corresponding parts of congruent triangles are congruent.

Corresponding parts of congruent triangles are congruent.

Corresponding Parts of Congruent Triangles are Congruent.

If you can prove congruence using a shortcut, then you KNOW that the remaining corresponding parts are congruent.

CPCTC

You can only use CPCTC in a proof AFTER you have proved congruence.

AC DF Given

⦟C ⦟ F Given

CB FE Given

ΔABC ΔDEF SAS

AB DE CPCTC

For example:

A

Prove: AB DE

B

C

D

F

E

ABCCDA

STATEMENTS

REASONS

S

BC DA

Given

Given

A

Alternate Interior Angles Theorem

S

ACCA

Reflexive Property of Congruence

EXAMPLE 2

Use the SAS Congruence Postulate

CW: Write a proof.

GIVEN

PROVE

Use the SAS Congruence Postulate

STATEMENTS

REASONS

ABCCDA

SAS Congruence Postulate

what did you learn today?

what was easy? what was difficult?