# Parallel And Perpendicular Lines Worksheet Page 10

Angles and Parallel Lines
Use the properties of parallel lines to determine congruent angles.
Use algebra to find angle measures.
C03-041C
can angles and lines be used in art?
can angles and lines be used in art?
In the painting, the artist uses lines
and transversals to create patterns.
The figure on the painting shows two
parallel lines with a transversal
passing through them. There is a
special relationship between the angle
1 1
1
pairs formed by these lines.
2 2
2
The Order of Tradition II by T.C. Stuart
PARALLEL LINES AND ANGLE PAIRS
In the figure above,
1 and
2 are
corresponding angles. When the two lines are parallel, there is a special relationship
between these pairs of angles.
Postulate 3.1
Postulate 3.1
Corresponding Angles Postulate
If two parallel lines are cut by a
1
2
transversal, then each pair of corresponding angles is congruent.
3
4
Examples:
1
5,
2
6,
3
7,
4
8
5
6
7
8
Study Tip
Determine Angle Measures
Example
Example
1
1
Look Back
In the figure, m 3
133. Find m 5.
To review vertical angles,
4
1
see Lesson 1-6.
3
7
Corresponding Angles Postulate
3
2
7
5
Vertical Angles Theorem
8
5
k
3
5
Transitive Property
7
6
m 3
m 5
Definition of congruent angles
133
m 5
Substitution
In Example 1, alternate interior angles 3 and 5 are congruent. This suggests
another special relationship between angles formed by two parallel lines and a
transversal. Other relationships are summarized in Theorems 3.1, 3.2, and 3.3.
Lesson 3-2 Angles and Parallel Lines 133
Carey Kingsbury/Art Avalon