Transcript Get Ready for Chapter 3  P.125 1-11 3-1 PARALLELS I.

Get Ready for Chapter 3
 P.125 1-11
3-1 PARALLELS
I. PARALLEL LINES
II. INTERSECTING LINES
III. SKEW LINES
IV. TRANSVERSALS
EXAMPLES
1. Name the plane parallel to plane AEF
2. Which segment is skew to GH?
3. How many segments intersect
AM?
4. Name a pair of consecutive
interior angles
5. Which statement is true
about skew lines?
A.They intersect
B.They lie in the same plane.
C.They are perpendicular
D.They do not intersect.
6. Identify:
 a. Name all planes
that are parallel to
plane ABC.
 b. Name all segments
that intersect AB.
 c. Name all segments
that are parallel to KG.
 d. Name all segments
that are skew to TK.
 7. Texas is the leading producer of livestock
in the United States. A diagram of a feed lot
on a farm is shown below. Identify the sets of
lines to which each given line is a
transversal.
 a. line k
b.
line s
c.
line p
 d. line m
8. Refer to the figure below. Identify each pair
of angles as alternate interior, alternate
exterior, corresponding, or consecutive interior
angles.






a.
b.
c.
d.
e.
f.
2 and 10
9 and 7
1 and 7
12 and 8
11 and 8
4 and 12
Classwork
 P. 128 1-21
3-2
ANGLES
Corresponding angles
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles
are congruent.
1
2
1
2
Alternate Interior
If two parallel lines are cut by a transversal,
then the pairs of alternate interior angles are
congruent.
3
4
3
4
Consecutive Interior
If two parallel lines are cut by a transversal,
then the pairs of consecutive interior angles are
supplementary.
5
6
m
5+m
6 = 180°
Alternate Exterior
If two parallel lines are cut by a transversal,
then the pairs of alternate exterior angles are
congruent.
7
8
7
8
Perpendicular transversal
If a transversal is perpendicular to one of two parallel
lines, then it is perpendicular to the other.
j
k
Examples
1. If < 3 = 108, find all other angles.
A
1 2
5 6
C
B
3
7
4
D
8
2. Use properties of
parallel lines to find
the value of x.
SOLUTION
m
m
4 = 125°
4 + (x + 15)° = 180°
125° + (x + 15)° = 180°
x = 40°
Corresponding Angles Postulate
Linear Pair Postulate
Substitute.
Subtract.
3. Find the measure of <1 if
< 1 = 8y – 6 and < 2 = 7y.
4. Find y.
5. If < 2 = 8x = 6 and
<6 = 4x + 28, find x and <
6.
6. In the figure, m4 = 121.
Find m5.
7. What is the measure of
ABC?
8. If m1 = 16x - 8, m2 = 4(y +
8), and m3 = 14x + 2, find x and
y.