Geometry Section 3.3 part 2: Partial Proofs Involving Parallel Lines

We will do proofs in two columns We will do proofs in two columns. In the left-hand column, we will write statements which will lead from the given information (the given information is always listed as the first statement) down to what we need to prove (what we need to prove will always be the last statement). In the right-hand column, we must give a reason why each statement is true. The reason for the first statement will always be ________, and the reason for each of the other statements must be a _________, ________ or _________.

Let’s review the definitions, postulates and theorems we will use in our proofs.

Angle bisector: An angle bisector is Supplementary angles: Two angles are supplementary if

Postulates: Corresponding Angles Postulate (CAP): If _________________ are cut by a transversal, then __________________________________ Linear Pair Postulate (LPP): If two angles form a linear pair, then _______________________ *Substitution:

Theorems: Vertical Angle Theorem (VAT): If two angles are vertical angles, then _____________________ Alternate Interior Angle Theorem (AIAT): If two parallel lines are cut by a transversal, then ______________________________________ Alternate Exterior Angle Theorem (AEAT): If two parallel lines are cut by a transversal, then ______________________________________ Same-side Interior Angle Theorem (SSIAT): If two parallel lines are cut by a transversal, then ______________________________________

Here are some suggestions that may help you when doing proofs. 1 Here are some suggestions that may help you when doing proofs. 1. Reason backwards when possible. 2. Consider each piece of given information separately, and make any conclusion(s) that follow(s). 3. You will have to write at least one statement based on the figure – you are looking for one of the special angle pairs listed at the beginning of the definition section. 4. You will use the substitution postulate in almost every proof that you do – WATCH FOR IT!!!!