Geometry Section 3.3 part 2:
Partial Proofs Involving Parallel Lines
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 ________,
Given and the reason
for each of the other statements must be a _________,
Definition
________
Theorem
Postulate or _________.
Let’s review the definitions, postulates and
theorems we will use in our proofs.
Definitions:
Vertical angles
Linear Pairs
Corresponding Angles
Alternate interior angles
Alternate exterior angles
Same-side interior angles
Use these definitions when you make a statement that a pair of
angles in the figure is one of these special angle pairs.
Angle bisector: An angle bisector is
a ray that divides the angle into two congruent angles.
Supplementary angles: Two angles are supplementary if
they have a sum of 180.
Postulates:
Corresponding Angles Postulate (CAP): If
_________________
two parallel lines are cut by a transversal, then
__________________________________
corresponding angles are congruent.
Linear Pair Postulate (LPP): If two angles form a linear
pair, then _______________________
they are supplementary.
*Substitution:
If two quantities are equal, then one may be substituted
for the other in any equation or inequality.
Theorems:
Vertical Angle Theorem (VAT): If two angles are vertical angles, then
_____________________
they are congruent.
Alternate Interior Angle Theorem (AIAT): If two parallel lines are cut
alternate interior angles are congruent.
by a transversal, then ______________________________________
Alternate Exterior Angle Theorem (AEAT): If two parallel lines are cut
by a transversal, then alternate
______________________________________
exterior angles are congruent.
Same-side Interior Angle Theorem (SSIAT): If two parallel lines are cut
- side interior angles are congruent.
by a transversal, then same
______________________________________
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!!!!