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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.

Answer in a complete sentence on your warm–up paper:

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.

Homework due today

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

Chapter 4 Triangles

Chapter 4 Triangles--

Proving Triangles Congruent

F

B

A

C

E

D

The Idea of a Congruence

Two geometric figures with exactly the same size and shape.

How much do you

need to know. . .

. . . about two triangles

to prove that they

are congruent?

Corresponding Parts

- 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

SSS

SAS

ASA

AAS

Do you need all six ?

NO !

Side-Side-Side (SSS)

E

B

F

A

D

C

- AB DE
- BC EF
- AC DF

ABC DEF

Side-Angle-Side (SAS)

B

E

F

A

C

D

- AB DE
- A D
- AC DF

ABC DEF

included

angle

Included Angle

The angle between two sides

H

G

I

E

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

Included Side

The side between two angles

GI

GH

HI

E

Y

S

Included Side

Name the includedside:

Y and E

E and S

S and Y

YE

ES

SY

Angle-Angle-Side (AAS)

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

Name That Postulate

(when possible)

SAS

ASA

SSA

SSS

Name That Postulate

(when possible)

AAA

ASA

SSA

SAS

Name That Postulate

(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)

Let’s Practice

ACFE

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

For ASA:

B D

For SAS:

AF

For AAS:

CW

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

For ASA:

For SAS:

For AAS:

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B

F

That means that EG CB

A

E

What is AC congruent to?

FE

G

C

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.

Statements Reasons

AC DF Given

⦟C ⦟ F Given

CB FE Given

ΔABC ΔDEF SAS

AB DE CPCTC

A

Prove: AB DE

B

C

D

F

E

BC DA,BC AD

ABCCDA

STATEMENTS

REASONS

S

BC DA

Given

Given

BC AD

BCADAC

A

Alternate Interior Angles Theorem

S

ACCA

Reflexive Property of Congruence

EXAMPLE 2

Use the SAS Congruence Postulate

CW: Write a proof.

GIVEN

PROVE

EXAMPLE 2

Use the SAS Congruence Postulate

STATEMENTS

REASONS

ABCCDA

SAS Congruence Postulate

what did you learn today?

what was easy? what was difficult?

what can I do to help you?