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

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

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

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

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

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

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

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

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

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

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

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