Transcript m 3

3-3 Proving Lines Parallel
Warm Up
State the converse of each statement.
1. If a = b, then a + c = b + c.
2. If mA + mB = 90°, then A and B are
complementary.
3. If AB + BC = AC, then A, B, and C are collinear.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Objective
Use the angles formed by a transversal
to prove two lines are parallel.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Recall that the converse of a theorem is
found by exchanging the hypothesis and
conclusion. The converse of a theorem is not
automatically true. If it is true, it must be
stated as a postulate or proved as a separate
theorem.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 1A: Using the Converse of the
Corresponding Angles Postulate
Use the Converse of the Corresponding Angles
Postulate and the given information to show
that ℓ || m.
4  8
4  8
ℓ || m
Holt McDougal Geometry
4 and 8 are corresponding angles.
Conv. of Corr. s Post.
3-3 Proving Lines Parallel
Example 1B: Using the Converse of the
Corresponding Angles Postulate
Use the Converse of the Corresponding Angles
Postulate and the given information to show
that ℓ || m.
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30
m3 = 4(30) – 80 = 40
m8 = 3(30) – 50 = 40
m3 = m8
3  8
ℓ || m
Holt McDougal Geometry
3-3 Proving Lines Parallel
The Converse of the Corresponding Angles
Postulate is used to construct parallel lines.
The Parallel Postulate guarantees that for any
line ℓ, you can always construct a parallel line
through a point that is not on ℓ.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Holt McDougal Geometry
3-3 Proving Lines Parallel
Example 2B: Determining Whether Lines are Parallel
Use the given information and the theorems you
have learned to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 3)°, x = 5
m2 = 10x + 8
= 10(5) + 8 = 58
Substitute 5 for x.
m3 = 25x – 3
= 25(5) – 3 = 122
Substitute 5 for x.
Holt McDougal Geometry
3-3 Proving Lines Parallel
Use the given information and the theorems you
have learned to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 3)°, x = 5
m2 = 10x + 8
= 10(5) + 8 = 58
m3 = 25x – 3
= 25(5) – 3 = 122
m2 + m3 = 58° + 122°
= 180°
r || s
Holt McDougal Geometry
.
3-3 Proving Lines Parallel
Given: p || r , 1  3
Prove: ℓ || m
Statements
Reasons
1. p || r
1. Given
2. 3  2
2. Alt. Ext. s Thm.
3. 1  3
3. Given
4. 1  2
4. Trans. Prop. of 
5. Conv. of Corr. s Post.
5. ℓ ||m
Holt McDougal Geometry
3-3 Proving Lines Parallel
Check It Out! Example 3
Given: 1  4, 3 and 4 are supplementary.
Prove: ℓ || m
Holt McDougal Geometry
3-3 Proving Lines Parallel
Check It Out! Example 3 Continued
Statements
1.
2.
3.
4.
5.
6.
7.
1  4
m1 = m4
3 and 4 are supp.
m3 + m4 = 180
m3 + m1 = 180
m2 = m3
m2 + m1 = 180
8. ℓ || m
Holt McDougal Geometry
Reasons
1. Given
2. Def.  s
3. Given
4. Trans. Prop. of 
5. Substitution
6. Vert.s Thm.
7. Substitution
8. Conv. of Same-Side
Interior s Post.
3-3 Proving Lines Parallel
Classwork/Homework
• Pg. 166 (1-22 all)
Holt McDougal Geometry