1. Proving Triangles Congruent Corresponding parts of congruent triangles
Proofs
Proving Triangles Congruent
Corresponding parts of congruent triangles

2. Two Column or Paragraph
For every statement there needs to be a reason you can say it Statement – equations Reason – definitions Need to have enough pieces proven congruent to prove triangles congruent by SSS, SAS, ASA

3. Two Column Proof Broken into 3 parts Given
Make sure you have 3 congruent parts
Congruency statement and conjecture

4. Paragraph Proof
Using similar ideas as the two column proof but explaining in sentences. You still need to be able to support everything that you are saying with terms and conjectures

5. Doing a Proof
You normally have a picture to go along with the proof. As you state things congruent mark them in the picture As you state things congruent write S or A next to the statement, this helps you keep track of how many parts you have congruent

6. More on Proofs
When writing a proof you will usually need a minimum of 4 statements and reasons. 3 of them are to state sides or angles congruent 1 of them is to state triangles congruent and why

7. Statement Reason EC = AC Given ER = AR RC = RC Reflexive REC = RAC SSS
Prove the Triangles Congruent
Statement
Reason
EC = AC
Given
ER = AR
RC = RC
Reflexive
REC = RAC
SSS

8. Examples Given: Prove: Statement Reason AB=CD <ABC=<DCB BC=BC

9. Statements
Anything that is told to you in the problem should be written down segment AB bisects segment DC M is the midpoint When adding things together such as angles or a triangle Stating things congruent because of parallel lines

10. Pictures
It may also help to redraw and label the pictures so they are easier to see what you are trying to prove. Mark parts you proved congruent in the picture to help keep track of what you have It may also be helpful to label these in the proof itself

11. Reasoning
Why you are writing the statements Given information Terms we have used on why angles are congruent – vertical angles, AI, AE, Corr if lines are parallel Midpoint proves two segments congruent Angle Bisector, Perpendicular Bisector Reflexive – means it is a side or angle that is used in both triangles Substitution – putting one value in place of another to solve

12. Example Given: Segment WX and segment YZ bisect each other
Prove: the two triangles are congruent