1. Ch 4.4 Proving Lines Parallel
Learning Target:
I will be able to recognize angle pairs that occur with parallel lines and prove that two lines are parallel using angle relationships.
Standard 7.0
Students prove and use theorems involving the properties of parallel lines cut by a transversal.

2. Ch 4.4
Postulate 4-2
Concept

3. Ch 4.4
Postulate 4-2.5
Concept

4. Ch 4.4
4-5
4-6
4-7
4-8
Concept

5. Ch 4.4
Identify Parallel Lines
A. Given 1  3, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.
1 and 3 are corresponding angles of lines a and b.
Answer: Since 1  3, a║b by the Converse of the Corresponding Angles Postulate.
Example 1

6. Ch 4.4
Identify Parallel Lines
B. Given m1 = 103 and m4 = 100, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.
1 and 4 are alternate interior angles of lines a and c.
Answer: Since 1 is not congruent to 4, line a is not parallel to line c by the Converse of the Alternate Interior Angles Theorem.
Example 1

7. Ch 4.4
Classwork #1
A. Given 1  5, is it possible to prove that any of the lines shown are parallel?
A. Yes; ℓ ║ n
B. Yes; m ║ n
C. Yes; ℓ ║ m
D. It is not possible to prove any of the lines parallel.
Example 1

8. Ch 4.4
Classwork #1
B. Given m4 = 105 and m5 = 70, is it possible to prove that any of the lines shown are parallel?
A. Yes; ℓ ║ n
B. Yes; m ║ n
C. Yes; ℓ ║ m
D. It is not possible to prove any of the lines parallel.
Example 1

9. Ch 4.4 Find mZYN so that || . Show your work.
Read the Test Item From the figure, you know that mWXP = 11x – 25 and mZYN = 7x You are asked to find mZYN.
Example 2

10. Ch 4.4
Solve the Test Item WXP and ZYN are alternate exterior angles. For line PQ to be parallel to line MN, the alternate exterior angles must be congruent. So mWXP = mZYN. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find mZYN.
m WXP = m ZYN Alternate exterior angles
11x – 25 = 7x + 35 Substitution
4x – 25 = 35 Subtract 7x from each side.
4x = 60 Add 25 to each side.
x = 15 Divide each side by 4.
Example 2

11. Ch 4.4 Now use the value of x to find mZYN.
mZYN = 7x + 35 Original equation
= 7(15) + 35 x = 15
= 140 Simplify.
Answer: mZYN = 140
Check Verify the angle measure by using the value of x to find mWXP.
mWXP = 11x – 25
= 11(15) – 25
= 140
Since mWXP = mZYN, WXP  ZYN and ||
Example 2

12. Ch 4.4 Classwork #2 ALGEBRA Find x so that || . A. x = 60 B. x = 9
C. x = 12
D. x = 12
Example 2

13. Ch 4.4
Prove Lines Parallel
CONSTRUCTION In the window shown, the diamond grid pattern is constructed by hand. Is it possible to ensure that the wood pieces that run the same direction are parallel? If so, explain how. If not, explain why not.
Answer: Measure the corresponding angles formed by two consecutive grid lines and the intersecting grid line traveling in the opposite direction. If these angles are congruent, then the grid lines that run in the same direction are parallel by the Converse of the Corresponding Angles Postulate.
Example 3

14. Ch 4.4
Classwork #3
GAMES In the game Tic-Tac-Toe, four lines intersect to form a square with four right angles in the middle of the grid. Is it possible to prove any of the lines parallel or perpendicular? Choose the best answer.
A. The two horizontal lines are parallel.
B. The two vertical lines are parallel.
The vertical lines are perpendicular to the horizontal lines.
All of these statements are true.
Example 3