Transcript Properties of Parallel Lines LESSON 3-1 Additional Examples Use the diagram above. Identify which angle forms a pair of same-side interior angles with 1.

Properties of Parallel Lines
LESSON 3-1
Additional Examples
Use the diagram above. Identify which angle forms a pair of same-side
interior angles with 1. Identify which angle forms a pair of corresponding
angles with 1.
Same-side interior angles are on the same side of transversal t
between lines p and q.
4, 8, and 5 are on the same side of the transversal as
but only 1 and 8 are interior.
So
HELP
1 and
1,
8 are same-side interior angles.
GEOMETRY
Properties of Parallel Lines
LESSON 3-1
Additional Examples
(continued)
Corresponding angles also lie on the same side of the transversal.
One angle must be an interior angle, and the other must be an exterior angle.
The angle corresponding to 1 must lie in the same position relative to
line q as 1 lies relative to line p. Because 1 is an interior angle, 1 and
are corresponding angles.
5
Quick Check
HELP
GEOMETRY
Properties of Parallel Lines
LESSON 3-1
Additional Examples
Compare 2 and the vertical angle of 1. Classify the angles
as alternate interior angles, same-side interior angles, or
corresponding angles.
The vertical angle of
1 is between the parallel runway segments.
2 is between the runway segments and on the opposite side of
the transversal runway.
Because alternate interior angles are not adjacent and lie between
the lines on opposite sides of the transversal, 2 and the vertical angle
of 1 are alternate interior angles.
Quick Check
HELP
GEOMETRY
Properties of Parallel Lines
LESSON 3-1
Additional Examples
Use the given that a b and the diagram to write a two-column proof
that 1 and 4 are supplementary.
Statements
Reasons
1. a  b
1. Given
2. m 1 = m 3
2. Corresponding Angles Postulate
3. m 3 + m 4 = 180
3. Angle Addition Postulate
4. m 1 + m 4 = 180
4. Substitution
5. 1 and 4 are
supplementary
5. Definition of supplementary angles
HELP
Quick Check
GEOMETRY
Properties of Parallel Lines
LESSON 3-1
Additional Examples
In the diagram above,
|| m. Find m 1 and then m
2.
1 and the 42° angle are corresponding angles. Because
m 1 = 42 by the Corresponding Angles Postulate.
|| m,
Because 1 and 2 are adjacent angles that form a straight angle,
m 1 + m 2 = 180 by the Angle Addition Postulate.
If you substitute 42 for m 1, the equation becomes 42 + m
Subtract 42 from each side to find m 2 = 138.
2 = 180.
Quick Check
HELP
GEOMETRY
Properties of Parallel Lines
LESSON 3-1
Additional Examples
In the diagram above,
|| m. Find the values of a, b, and c.
a = 65
Alternate Interior Angles Theorem
c = 40
Alternate Interior Angles Theorem
a + b + c = 180
65 + b + 40 = 180
b = 75
Angle Addition Postulate
Substitution Property of Equality
Subtraction Property of Equality
Quick Check
HELP
GEOMETRY