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4.3- Proving Triangles are Congruent: SSS & SAS Proving... · Postulate 20-Side-Angle-Side (SAS)...

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Bell Ringer: Why can’t two triangles be proven congruent based solely on their angle measurements?

Transcript

Bell Ringer:

Why can’t two triangles be

proven congruent based solely on

their angle measurements?

Bell Ringer:

Why can’t two triangles be

proven congruent based solely on

their angle measurements?

At least one set of sides must be

congruent.

Daily Learning Target:

“I can prove triangles congruent

by their sides and angles with

SSS and SAS methods.”

How much do you need to know?

• To prove two triangles are exactly alike? (congruent)

• If all 6 parts (3 corresponding sides and 3 corresponding angles) are congruent….that would do it.

• Any “shortcuts”?

Postulate 19-Side Side Side

(SSS) Congruence Postulate

• If three sides of one

triangle are congruent

to three sides of

another triangle

• Then the two triangles

are congrurent.

• The remaining parts

are congruent. Side CADOSide CTDGSide ATOG

CAT DOG

G

O

D

T

A

C

Postulate 20-Side-Angle-Side

(SAS) Congruence Postulate

• If two sides and the

included angle of one

triangle are congruent

to two sides and the

included angle of

another triangle…

• Then the triangles

are congruent. Side CADOAngle AOSide ATOG

CAT DOG

G

O

D

T

A

C

Use the diagram. Name the

included angle between the pair of

sides given.

Use the diagram. Name the

included angle between the pair of

sides given.

For each pair of congruent

triangles, name the pairs of

corresponding sides.

For each pair of congruent

triangles, name the pairs of

corresponding sides.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Decide whether enough information is given

to prove the triangles are congruent. If there

is enough information, state the congruence

postulate you would use.

Are these triangles congruent?

• By what

rule?

• Could you

use the

distance

formula

to verify

your

claim?

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

DE

F

C

BA

Assignment 4.1

Pages 208-211

(4-9, 20-25, 44-46)

Closing Activity: Whiteboards

In the SAS method of proving

triangles congruent, is the A part

between or outside the S’s?

Closing Activity: Whiteboards

In the SAS method of proving

triangles congruent, is the A part

between or outside the S’s?

Between

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