Warm ups

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

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

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

3-5 PROVING LINES PARALLELObjective: Recognize angle pairs that occur with parallel lines. Prove that two lines are parallel.

Converse of Corresponding Angles Postulate

Parallel Postulate

Example 1A. 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.

Identify Parallel Lines

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.

Example 1B. 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.

Identify Parallel Lines

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.

TOO

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?

TOO

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 m<4 = 105 and m<5 = 70, is it possible to prove that any of the lines shown are parallel?

Example 2Find m<ZYN so that || . Show your work.

Use Angle Relationships

TOOALGEBRA Find x so that || .

A. x = 60

B. x = 9

C. x = 12

D. x = 12

Example 3

A. The two horizontal lines are parallel.

B. The two vertical lines are parallel.

C. The vertical lines are perpendicular to the horizontal lines.

D. All of these statements are true.

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.

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