4-2: Triangle Congruence by SSS and SAS

4-3: Triangle Congruence by ASA and AAS

4-4: Using Corresponding Parts of Congruent Triangles

Side-Side-Side (SSS)

If, in two triangles: three sides of one are congruent to

three sides of the other, then the triangles are congruent.

A

B

C

D

E

F

Side-Angle-Side (SAS)

If, in two triangles: two sides and the included angle

of one are congruent to two sides and the included angle of the other, then the triangles are congruent

A

B

C

D

E

F

Angle-Side-Angle (ASA)

If, in two triangles: two angles and the included side

of one are congruent to two angles and the included side of the other, then the two triangles are congruent.

A

B

C

D

E

F

Angle-Angle-Side (AAS) If, in two triangles:

two angles and a non-included side of one are congruent respectively to two angles and the corresponding non-included side of the other, then the triangles are congruent.

A

B

C

D

E

F

Using only the given information, which pairs of triangles are congruent? Justify your answer.

1.2.

3.

Yes; SAS

No

No

Writing Proofs

Prove ___ parts of one triangle are ____________ to the _________________ parts of another triangle.

Use Triangle Congruence Theorems and other theorems in the proof.

congruent

3corresponding

3

Ex. 1

Statement Reason

Given:

Prove:

N is the midpoint of UC

U C FUN ACN

F

U

N

A

C

1). Given

1). N is the midpoint of UC

U C

Ex. 2

Statement

Reason

Given:

Prove:

90 , 90

and

m PLT m LTO

LP TO

LTO TLP

L

T

P

O

1). Given1).

90 , 90

and

m PLT m LTO

LP TO

Ex. 3

Statement Reason

Given:

Prove:

bisects AE BAD

B D

88888888888888

ABC ADC

1). Given1).

bisects AE BAD

B D

88888888888888

A

B C D

E

Ex. 4

Statement

Reason

Given:

Prove:

and KJ ML KJ LM:8:88:88:88:88:88:88:88:88:88:88:88:88:8 8:8

KJL LMK

1). Given1).

and KJ ML KJ LM:8:88:88:88:88:88:88:88:88:88:88:88:88:8 8:8

JK

LM

If two figures are congruent, then so are all of their corresponding parts.

Corresponding Parts of Congruent Figures are Congruent (CPCFC)

Ex. 5

Given:

Prove:

1 3; 2 4

WA IT

Statement

Reason

1). Given1).

1 3; 2 4

W A

IT

12

3 4