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Five-Minute Check (over Lesson 3–4)

CCSS

Then/Now

Postulate 3.4: Converse of Corresponding Angles Postulate

Postulate 3.5: Parallel Postulate

Theorems: Proving Lines Parallel

Example 1: Identify Parallel Lines

Example 2: Standardized Test Example: Use Angle Relationships

Example 3: Real-World Example: Prove Lines Parallel

Over Lesson 3–4

A.

B.

C.

D.

containing the point (5, –2) in point-slope form?

Over Lesson 3–4

A. y = 3x + 7

B. y = 3x – 2

C. y – 7 = 3x + 2

D. y – 7 = 3(x + 2)

What is the equation of the line with slope 3 containing the point (–2, 7) in point-slope form?

Over Lesson 3–4

A. y = –3x + 2.5

B. y = –3x

C. y – 2.5 = –3x

D. y = –3(x + 2.5)

What equation represents a line with slope –3 containing the point (0, 2.5) in slope-intercept form?

Over Lesson 3–4

A.

B.

C.

D.

containing the point (4, –6) in slope-intercept form?

Over Lesson 3–4

A. y = 3x + 2

B. y = 3x – 2

C. y – 6 = 3(x – 2)

D. y – 6 = 3x + 2

What equation represents a line containing points (1, 5) and (3, 11)?

Over Lesson 3–4

A.

B.

C.

D.

Content Standards

G.CO.9 Prove theorems about lines and angles.

G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Mathematical Practices

1 Make sense of problems and persevere in solving them.

3 Construct viable arguments and critique the reasoning of others.

You found slopes of lines and used them to identify parallel and perpendicular lines.

• Recognize angle pairs that occur with parallel lines.

• Prove that two lines are parallel.

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.

Answer: Since 1 3, a║b by the Converse of the Corresponding Angles Postulate.

1 and 3 are corresponding angles of lines a and b.

Identify Parallel Lines

B. Given m1 = 103 and m4 = 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.

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.

1 and 4 are alternate interior angles of lines a and c.

A. Yes; ℓ ║ n

B. Yes; m ║ n

C. Yes; ℓ ║ m

D. It is not possible to prove any of the lines parallel.

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.

B. Given m4 = 105 and m5 = 70, is it possible to prove that any of the lines shown are parallel?

Find mZYN so that || . Show your work.

Read the Test Item From the figure, you know that mWXP = 11x – 25 and mZYN = 7x + 35. You are asked to find mZYN.

Use Angle Relationships

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.

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. SomWXP = mZYN. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find mZYN.

Use Angle Relationships

Now use the value of x to find mZYN.

mZYN = 7x + 35 Original equation

Answer: mZYN = 140

= 7(15) + 35 x = 15

= 140 Simplify.

Check Verify the angle measure by using the value of x to find mWXP.

mWXP = 11x – 25

Since mWXP = mZYN, WXP ZYN and || .

= 11(15) – 25

= 140

Use Angle Relationships

ALGEBRA Find x so that || .

A. x = 60

B. x = 9

C. x = 12

D. x = 12