proving triangles congruent
Download
Skip this Video
Download Presentation
Proving Triangles Congruent

Loading in 2 Seconds...

play fullscreen
1 / 32

Proving Triangles Congruent - PowerPoint PPT Presentation


  • 95 Views
  • Uploaded on

Proving Triangles Congruent. F. B. A. C. E. D. What does it mean for 2 triangles to be congruent?. Corresponding angles and sides should have the same measure . How much do you need to know. . . . . . about two triangles to prove that they

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Proving Triangles Congruent' - burian


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2

F

B

A

C

E

D

What does it mean for 2 triangles to be congruent?

Corresponding angles and sides should have the same measure.

slide3

How much do you

need to know. . .

. . . about two triangles

to prove that they

are congruent?

slide4

Corresponding Parts

  • AB DE
  • BC EF
  • AC DF
  •  A  D
  •  B  E
  •  C  F

B

A

C

E

F

D

If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.

ABC DEF

slide5

SSS

SAS

ASA

AAS

Do you need all six ?

NO !

slide7

What if we have all three angles?

  • Use your protractor to draw Triangle ABC., so that:
  • Angle A measures 70º,
  • Angle B measures 30º and
  • Angle C measures 80º.
  • Now measure the lengths of the sides of your triangle.
  • Compare your results with your partner. Are your triangles congruent?
slide8

Does AAA work?

No, the angles will be the same, but the triangles don’t have to be congruent.

slide9

Will 3 sides be enough for congruence?

  • Make a triangle DEF so that:
  • DE is 5 cm
  • EF is 8 cm
  • DF is 12 cm
  • Now measure the angles. Compare your results with your partner. Are your triangles congruent?
slide10

Side-Side-Side (SSS)

SSS Congruence Conjecture

If the 3 sides of one triangle are congruent to the 3 sides of another triangle then the triangles are congruent.

slide11

Side-Side-Side (SSS)

E

B

F

A

D

C

  • AB DE
  • BC EF
  • AC DF

ABC DEF

slide12

Side-Angle-Side (SAS)

SAS Congruence Conjecture

If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle then the triangles are congruent.

slide13

Side-Angle-Side (SAS)

B

E

F

A

C

D

  • AB DE
  • A D
  • AC DF

ABC DEF

included

angle

slide14

Included Angle

The angle between two sides

G

slide15

E

Y

S

Included Angle

Name the included angle:

YE and ES

ES and YS

YS and YE

E

S

Y

slide16

Included Side

The side between two angles

GH

slide17

E

Y

S

Included Side

Name the included angle:

Y and E

E and S

S and Y

YE

ES

SY

slide18

Angle-Side-Angle (ASA)

ASA Congruence Conjecture

If 2 angles and the included side of one triangle is congruent to two angles and the included side of another triangle, then the triangles are congruent.

slide19

Angle-Side-Angle (ASA)

B

E

F

A

C

D

  • A D
  • AB  DE
  • B E

ABC DEF

included

side

slide20

Angle-Angle-Side (AAS or SAA)

AAS Congruence Conjecture

If 2 angles and a non-included side of one triangle is congruent to the corresponding angles and side of another triangle, then the triangles are included

slide21

Angle-Angle-Side (AAS)

B

E

F

A

C

D

  • A D
  • B E
  • BC  EF

ABC DEF

Non-included

side

slide22

Warning: No SSA Postulate

There is no such thing as an SSA postulate!

E

B

F

A

C

D

NOT CONGRUENT

slide23

Warning: No AAA Postulate

There is no such thing as an AAA postulate!

E

B

A

C

F

D

NOT CONGRUENT

slide24

SSS correspondence

  • ASA correspondence
  • SAS correspondence
  • AAS correspondence
  • SSA correspondence
  • AAA correspondence

The Congruence Postulates

slide25

Name That Postulate

(when possible)

SAS

ASA

SSA

SSS

slide26

Name That Postulate

(when possible)

AAA

ASA

SSA

SAS

slide27

Name That Postulate

(when possible)

Vertical Angles

Reflexive Property

SAS

SAS

Reflexive Property

Vertical Angles

SSA

SAS

slide30

Let’s Practice

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:

slide31

HW

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

For ASA:

For SAS:

For AAS:

slide32

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.

ad