4.4 Proving triangles using ASA and AAS

Angle-Side-Angle (ASA) postulate

• If 2 s and the included side of one Δ are to the corresponding s and included side of another Δ, then the 2 Δs are .

A

B

C

)

((

X

Y

Z

))

(

If A Z, C X and seg. AC seg. ZX, then Δ ABC Δ ZYX.

Angle-Angle-Side (AAS) theorem

• If 2 s and a non-included side of one Δ are to the corresponding s and non-included side of another Δ, then the 2 Δs are .

If A R, C S, and seg AB seg QR, then ΔABC ΔRQS.

((

))

)

)A

B

C

R

S

Q

ExamplesIs it possible to prove the Δs are

?

)

)) (

((

No, there is no AAA theorem!

))(

((

)

Yes, ASA

THERE IS NO AAA (TRAVEL AGENCY) OR BAD WORDS

Example• Given that B C, D F, M is the

midpoint of seg DF

• Prove Δ BDM Δ CFM

B

D M

C

F

) )

))

((

Example

• Given that seg WZ bisects XZY and XWY• Show that Δ WZX Δ WZY

((((

))

X

Z

Y

W

Once you know that Δs are , you can

state that their corresponding parts

are .

CPCTC• CPCTC-corresponding parts of triangles are .Ex: G: seg MP bisects

LMN, seg LM seg NMP: seg LP seg NP

( )

N

P

L

M