Geometry
Chapter 3 – Parallel and Perpendicular Lines Spring 2009
Section 3-1
Properties of Parallel Lines
Part I. Identifying Angle Pairs……………………………………
Transversal line is a line that ________________________________
_________________________________________________________
Interior Angles are the angles that lie _____________ the two lines
Exterior Angles are the angles that lie _____________ the two lines.
Alternate Angles are angles that lie on ______________ sides of the
transversal.
.
Same-Side Angles are angles that lie on the __________ side of the transversal line
Figure 1.
A. Angle Names. Using Figure 2, define special angle names:
Angles _______ and _______ are called Alternate Interior angles
(other Alternate Interior angle pairs: ______and ______)
Angles ______ and ________ are called Alternate Exterior angles.
(other Alternate Exterior angle pairs: ______and ______)
Angles ______ and ________ are called Same-Side Interior angles.
(other Same-side Interior angle pairs: ______and ______)
Angles ______ and ________ are called Same-Side Exterior angles.
(other Same-side Exterior angle pairs: ______and ______)
Figure 2.
Corresponding angles are angles that lie on the ____________________ of the transversal and in the same ____
______________ relative to each line. _________ and ________ are corresponding angles.
Name all other corresponding angle pairs: ______and_______,
______and________, ______and_______.
B. Student Activities: Determine which statements are true/false, using Figure 2.
1)____
2)____
3)____
4)____
5)____
6)____
7)____
8)____
Angles 1 and 4 are alternate interior angles.
Angles 2 and 7 are alternate interior angles.
Angles 5 and 3 are alternate exterior angles.
Angles 5 and 4 are alternate exterior angles.
Angles 3 and 2 are same-side interior angles.
Angles 3 and 7 are same-side interior angles.
Angles 5 and 8 are corresponding angles
Angles 5 and 7 are corresponding angles.
Activity: Measure angles with a protractor (separate sheet).
Challenge (after Part II of this worksheet):
Name all congruent angles in Figure 2.
Geometry
Chapter 3 – Parallel and Perpendicular Lines Spring 2009
Part II. Properties of Parallel Lines………………………………………
Suppose a ____________________ intersects two ________________ lines, then…..
Corresponding Angles Postulate (Property F).
corresponding angles are ______________.
Alternate Interior Angles Theorem (Property Z)
Alternate interior angles are _______________
Figure 3.
_____=_____
Figure 4.
_____ = _____
Same-Side Interior Angles Theorem(Property C)
same-side interior angles are ______________
Alternate Exterior Angles Theorem
alternate exterior angles are _____________
Figure 5.
_______+ _______=_____
Figure 6.
_______= _______
Part III. Finding Measures of Angles.………………………………………Assume the 2 lines are parallel
Find the measure of each designated angle and justify using a theorem or postulate.
1)
.
2)
2
40 o
1
By the: _______________________
m∠1=______ m∠2=_______
50 0
1
2
By the: _____________________________
m∠1=______ m∠2=_______
Geometry
Chapter 3 – Parallel and Perpendicular Lines Spring 2009
…
3)
2
3
4)
.
2
120o
1
1
By the: ___________________________
m∠1=______ m∠2=_______
m∠3=_______
20 o
By the: ________________________________
m∠1=______ m∠2=_______
Find the value of the variables
5)
.
6)
x
x-15
6y+20
2y