Download Warm up: In the figure, a b, and c is the transversal. 1. Which angle

Warm up:
In the figure, a b, and c is the transversal.
a
c
1
3 4 2
b
5
7 8 6
1. Which angle is a corresponding angle with 5?
2. Which angles are congruent to 2 and 3?
3. Find the measure of 8 if m 3 = 78.
4. Find the measure of 6 if m 2 = 84.
5. Find x if m 1 = 9x and m 5 = 6(x + 5).
1
Review for Quiz 4­1 & 4­2
1. Describe each pair of segments as parallel, skew or
intersecting.
X
a. BD and XZ
b. FY and ZY
c. BF and YZ
Y
B
F
Z
D
2. Find the measures of the angles.
a. Find m 16, if m 10 = 75
b. Find m 1, if m 13 = 83
6 5
7 8
c. Find m 8, if m 9 = 45
2 1
3 4
d. Find m 4, if m 14 = 133 10 9
11 12
14 13
15 16
2
3. Find the values of x and y.
(4y + 2)°
4x°
(x + 5)°
(2y + 8)°
OBJECTIVE: You will learn to identify conditions that produce parallel lines and to construct parallel lines.
Section 4­4 ______________
Postulate 4­2 In a plane, if two lines are cut by a transversal so
that a pair of corresponding angles is congruent,
then the lines are parallel.
1
a
2
b
If 1 = 2, then a b.
3
Example 1: If m 1 = 13x ­ 8 and m 2 = 12x + 4, find x so that l m.
l
2 3
1
m
Theorem 4­5 In a plane, if two lines are cut by a transversal so that a pair of alternate interior angles is
congruent, then the two lines are parallel.
Theorem 4­6 In a plane, if two lines are cut by a transversal so
that a pair of alternate exterior angles is
congruent, then the two lines are parallel.
Theorem 4­7 In a plane, if two lines are cut by a transversal so
that a pair of same­side interior angles is
supplementary, then the two lines are parallel.
4
Theorem 4­8 In a plane, if two lines are perpendicular to the same line, then the two lines are parallel.
5 ways to prove two lines are parallel
• show corresponding angles are congruent
• show alternate interior angles are congruent
• show alternate exterior angles are congruent
• show same­side interior angles are supplementary
• show that two lines in a plane are perpendicular to a third line
Example 2: Identify the parallel segments in the letter z.
A
40°
C
B
40°
D
Example 3: Find the value of x so BE TS.
B
E
(4x + 8)° (2x + 10)°
(5x + 2)°
T
S
5
Hands on Geometry p. 162
1. Use a straightedge to draw a line l and a point P not on l.
2. Draw a line t through P that intersects line l. Label the angle between the lines as 1.
3. Use a compass and a straightedge to construct an angle
congruent to 1 at P. Label this angle 2.
4. Extend the side of 2 to form line m (which is parallel to
line l ).
QUESTIONS:
1. What relationship do angles 1 and 2 have?
2. Use a ruler to measure the distance between lines l and m
at several places. Make a conjecture about the relationship between the lines.
Guided Practice:
Find x so that a b.
a
b
1. 2.
84°
a
10x°
5x°
3x°
b
6
Name the pairs of parallel lines or segments.
S
3. 4.
p
113°
Q
U
42°
42°
q
67°
68°
42°
r
R
T
s
Do you have any Vocab questions?
OBJECTIVE:
HOMEWORK: p. 166 ­ 167
# 9 ­ 20, 25 ­ 29
7