Proving Triangles Congruent

Proving Triangles Congruent

Two geometric figures with exactly the same size and shape.

The Idea of a CongruenceThe Idea of a Congruence

A C

B

DE

F

How much do you How much do you need to know. . .need to know. . .

. . . about two triangles to prove that they are congruent?

Corresponding PartsCorresponding Parts

ABC DEF

B

A C

E

D

F

1. AB DE

2. BC EF

3. AC DF

4. A D

5. B E

6. C F

Side-Side-Side (SSS)Side-Side-Side (SSS)

1. AB DE

2. BC EF

3. AC DF

ABC DEF

B

A

C

E

D

F

If all three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Side-Angle-Side (SAS)Side-Angle-Side (SAS)

1. AB DE

2. A D

3. AC DF

ABC DEF

B

A

C

E

D

F

included angle

The angle between two sides

Included AngleIncluded Angle

Name the included angle:

YE and ES

ES and YS

YS and YE

Included AngleIncluded Angle

SY

E

E

S

Y

The Congruence PostulatesThe Congruence Postulates

SSS correspondence

SAS correspondence

ASA correspondence

AAS correspondence

SSA correspondence

AAA correspondence

Name That PostulateName That Postulate

SASSAS

SSSSSSSSASSA

(when possible)

Name That PostulateName That Postulate(when possible)

SASASS

AAAAAA

SSASSA

Name That PostulateName That Postulate(when possible)

SASASS

SASSAS

SASASS

Reflexive Property

Vertical Angles

Vertical Angles

Reflexive Property SSSS

AA

You try! Name That PostulateYou try! Name That Postulate(when possible)

(when possible)You try! Name That PostulateYou try! Name That Postulate

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

For SAS:

Point X is the midpoint of AE and BD.

1. Which segments are congruent?

2. Why is <1 congruent to <2?

3. Why is triangle ACB congruent to triangle ECD?