Warm Up (on handout)

Hints on Proofs If two triangles share a side, then you will probably use the ______________ property. reflexive

Hints on Proofs If you have vertical angles, you will probably use __________ ______ in the proof. vertical angles

Hints on Proofs If you are given “midpoint” or “bisects”, then you WILL use __________________, _______________________, or ______________________ in the proof. def. of midpoint def. of segment bisector def. of angle bisector

Hints on Proofs If you are given parallel lines, then you will use _______________ _________ angle theorem. alternate interior

Hints on Proofs If you are proving parts of a triangle are congruent, then the proof will probably end with ____________. CPCTC

Ways to Prove Triangles are Congruent Rt. ∆s only SSS SAS ASA AAS HL

Same Side Int. Angle Postulate Linear Pair is Supplementary Corresponding Angle Theorem Definition of Supplementary Angles Alternate Int. Angle Theorem Perp. Lines form right angles   All right angles are congruent Converse S-S Int. Angle Postulate Def. of a right angle Converse Corresponding Angle Theorem Converse Alternate Int. Angle Theorem Vertical Angles are congruent Def. of a perpendicular bisector ASA Def. of a midpoint SAS Def. of Segment Bisector SSS Def. of Angle Bisector AAS HL Substitution CPCTC Reflexive Symmetric Third angle theorem Transitive

Steps to Proving : Mark the picture with : Decide if your triangles are congruent by: ____, _____, _____, _____, or _____ (write this down by the picture so you don’t forget – this will be your last step or your second to last step) If you mark it in the picture, you need to mention it in the proof 4. Must have 3 ≅ statements before saying the triangles are ≅ (one for each A or S) **The givens will either directly give you the ≅, or will help you get one

1. Statements Reasons  

2. Statements Reasons  

3. Statements Reasons  

4. Statements Reasons