Download m 3

3-3
Lines
Parallel
3-5 Proving
Showing
Lines
are Parallel
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
Geometry
3-5 Proving Lines Parallel
3-3
Objective
Use the angles formed by a transversal
to prove two lines are parallel.
Holt Geometry
3-5 Proving Lines Parallel
3-3
If two parallel lines are cut by a
transversal, then the corresponding
angles are congruent.
100
100
Corresponding Angles Converse:
If 2 lines are cut by a transversal so
the corresponding angles are
congruent
_______________,
then the lines
parallel
are ______________.
Holt Geometry
3-5 Proving Lines Parallel
3-3
If two parallel lines are cut by a
transversal, then the alternate
interior angles are congruent.
50
50
Alt. Interior Angles Converse:
If 2 lines are cut by a transversal
so the alternate interior angles are
congruent
______________,
then the
parallel
lines are _____________.
Holt Geometry
3-5 Proving Lines Parallel
3-3
If two parallel lines are cut by a
transversal, then the alternate
exterior angles are congruent.
60
60
Alt. Exterior Angles Converse:
If 2 lines are cut by a transversal
so the alternate exterior angles are
congruent
_____________,
then the
parallel
lines are ____________.
Holt Geometry
3-5 Proving Lines Parallel
3-3
If two parallel lines are cut by a
transversal, then the consecutive
interior angles are
supplementary.
80
100
Consecutive Angles Converse:
If 2 lines are cut by a transversal
so the consecutive interior angles
supplementary then the
are _______________,
parallel
lines are ___________.
Holt Geometry
3-5 Proving Lines Parallel
3-3
Example 1: Using the Converse of Angle
Relationships
A) Use the given information to identify the
relationship that could be used to show that ℓ || m.
4  8
Yes, ℓ || m because of the Converse of Corresponding
Holt Geometry
3-5 Proving Lines Parallel
3-3
B) Use the given information to identify the
relationship that could be used to show that ℓ || m.
(aka plug in the value of x and see if it gives you a true statement.)
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30
m3 = 4(30) – 80 = 40
m7 = 3(30) – 50 = 40
3  7
Yes, ℓ || m because of the Converse of Corresponding
Holt Geometry
3-5 Proving Lines Parallel
3-3
C) Use the given information to identify the
relationship that could be used to show that ℓ || m.
m7 = (4x + 26)°,
m2 = (5x + 12)°, x = 13
m7 = 4(13) + 26 = 78
m2 = 5(13) + 12 = 77
Substitute 13 for x.
Substitute 13 for x.
m7 = m2
ℓ is not parallel to m because alternate interior angles
should be congruent, and these two angles are not.
Holt Geometry
3-5 Proving Lines Parallel
3-3
D) Use the given information to identify the
relationship that could be used to show that ℓ || m.
m1 = (3x + 10)°,
m8 = (4x - 10)°, x = 20
m1 = 3(20) + 10 = 70
Substitute 13 for x.
m8 = 4(20) - 10 = 70Substitute 13 for x.
m1 = m8
Yes, ℓ || m because of the converse of
alternate exterior angles
Holt Geometry
3-5 Proving Lines Parallel
3-3
E) Use the given information to identify the relationship
that could be used to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 67)°, x = 5
m2 = 10x + 8
= 10(5) + 8 = 58
m3 = 25x – 67
= 25(5) – 67 = 58
m2 + m3 = 58° + 58°
= 116°
2 and 3 are same-side
interior angles.
So, r is not parallel to s because the angles should =180
Holt Geometry