After ∆’s are proven congruent, we can draw NEWNEWNEWNEW conclusions & use a new REASON sentence!

If ABC DEF∆ ≅ ∆

Proof 1:

Given: Given: Given: Given: AB ≅ DC , , , , AD ≅ BC

Prove: Prove: Prove: Prove: A C≅∡ ∡

Statements Reasons

You Try!

Given: Given: Given: Given: A is the midpoint of MT

A is the midpoint of SR

Prove: Prove: Prove: Prove: ≅∡ ∡M T

Statements Reasons

M

S

A

R

T

4.54.54.54.5

3.3 CPCTC and Circles Geo H

3.3

C

A B

F

D E

THE NEW REASON: ______________

B A

D C

A New TheoremA New TheoremA New TheoremA New Theorem

The circle is named: ______

______ is the center of the circle

______ a radius of the circle

A New A New A New A New PostulatePostulatePostulatePostulate

AUXILIARY LINES:

Given: AB AC≅

BD CD≅

Prove: ABD ACD≅∡ ∡ .

Explain in words to your partner

WITHOUT writing the full proof

pROOF 2:

Given: Given: Given: Given: P

B CD

⊙

is a midpoint of

Conclusion:Conclusion:Conclusion:Conclusion: CPB DPB≅∡ ∡ Statements Reasons

P C

B A

A

D

C B

D

C D B

P

A

Proof 3: Given: Given: Given: Given: ⊙O

∠T is comp. to ∠MOT

∠S is comp. to ∠POS

ProveProveProveProve: : : : ≅MO PO

Statements Reasons

In your own words:

What Does CPCTC stand for and how is it used

in a proof?

P R

M

O

T

S

K