Download 3.3 Notes part 2

Geometry
Unit II
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
postulate
____________, and the reason for each of the other statements must be a __________________,
Theorem
definition
_________________
or ________________.
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.
Linear pairs
A ray that divides an angle into two adjacent angles that
Angle bisector: An angles bisector is _______________________________________________________
Are
congruent.
____________________________________
Supplementary angles: Two angles are supplementary if ______________________________________
Two angles whose measures add up to 180 degrees
Postulates:
Two parallel lines
Corresponding Angles Postulate (CAP): If _____________________________
are cut by a transversal,
The pairs of corresponding angles are congruent
then ________________________________________
Their sum = 180 degrees
Linear Pair Postulate (LPP): If two angles form a linear pair, then ________________________________
Replacing one quantity with an equivalent one.
*Substitution: _________________________________________________________________________
Theorems:
They are congruent
Vertical Angle Theorem (VAT): If two angles are vertical angles, then ____________________________
The pairs
Alternate Interior Angle Theorem (AIAT): If two parallel lines are cut by a transversal, then ___________
Of AIA are congruent
______________________________________________
The pairs
Alternate Exterior Angle Theorem (AEAT): If two parallel lines are cut by a transversal, then __________
______________________________________________
Of AEA are congruent
The pairs
Same-side Interior Angle Theorem (SSIAT): If two parallel lines are cut by a transversal, then _________
Of SSIA are supplementary.
___________________________________________________
Given: a // c, b // d
Prove: 1  11
a
1 2
3 4
5 6
8 7
b
1. a II c, b II d
2. 1 and 5
Are corresponding angle
1  5
3. 
_______
5 and 11
4. _____
Alternative Exterior Angles
5  11
5. ________
Given
Def. of corrs. Angles
CAP
Def alt. ext angles
1  11
6. _________
Substitution
AEAT
c
9 10
12 11
d
Given: a // c, b // d
Prove: 1 and 10 are supplementary
a
1 2
3 4
5 6
8 7
b
1. a II c, b II d
Given
c
9 10
12 11
2.  7 & 10 Are same side interior angles
Def. same side INT Angle
3.  7 & 10 Are supplementary
SSIAT
4. m 7  m 10  180
Def. of supplementary angles
5.  1 &  7 Are Alt. ext. angles
6.
7.
8.
 1  7
AEAT
m 1  m 10  180
 1 & 10
Def. of Alt. Ext. Angles
Are supplementary
Substitution
Def. of supplementary
d
Given: BE // LD , BE bisects ABD
Prove: ABE  D
A
E
B
1. BE II LD, BE bisects angle ABD
2.  ABE   EBD
3.  EBD &  D Are Alt. Int. Angle
Given
Def of Ang. Bisector
Def. Alt. Int
4.  EBD   D
AIAT
5.  ABE   D
Substitution
L
D