Geometry Congruence

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1

Slide 1

Proving Triangles Congruent

Slide 2

The Idea of a Congruence

Two geometric figures with exactly the same size and shape.

Slide 3

How much do you

need to know. . .

. . . about two triangles

to prove that they

are congruent?

Slide 4

Corresponding Parts

In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.

ABC   DEF

Slide 5

Do you need all six ?

NO !

Slide 6

Side-Side-Side (SSS)

Slide 7

Side-Angle-Side (SAS)

AB  DE

A   D

AC  DF

ABC   DEF

B

A

C

E

D

F

included

angle

Slide 8

Included Angle

The angle between two sides

 G

 I

 H

Slide 9

Name the included angle:

YE and ES

ES and YS

YS and YE

Included Angle

 E

 S

 Y

Slide 10

Angle-Side-Angle (ASA)

A   D

AB  DE

 B   E

ABC   DEF

B

A

C

E

D

F

included

side

Slide 11

Included Side

The side between two angles

GI

HI

GH

Slide 12

Name the included angle:

Y and E

E and S

S and Y

Included Side

YE

ES

SY

Slide 13

Angle-Angle-Side (AAS)

A   D

 B   E

BC  EF

ABC   DEF

B

A

C

E

D

F

Non-included

side

Slide 14