Lesson 3 5 Proving Lines Parallel 5 Minute

Lesson 3 -5 Proving Lines Parallel

5 -Minute Check on Lesson 3 -4 Transparency 3 -5 Write an equation in point-slope form for each line. 1. line with slope ¾ containing (5, – 2) 2. line parallel to the line 3 x – y = 6 that contains (– 2, 7) Write an equation in slope-intercept form for each line. 3. line with slope – 3 containing (0, 2. 5) 4. line with slope – 1/2 containing (4, – 6) 5. line through (1, 5) and (3, 11) 6. Standardized Test Practice: Which of the following describes the line y = – 2/3 x + 6? A parallel to the line y = 3/2 x + 6 B perpendicular to the line y = – 3/2 x + 6 C x-intercept is 6; y-intercept is 9 D x-intercept is 9; y-intercept is 6

5 -Minute Check on Lesson 3 -4 Transparency 3 -5 Write an equation in point-slope form for each line. 1. line with slope ¾ containing (5, – 2) y + 2 = ¾(x – 5) 2. line parallel to the line 3 x – y = 6 that contains (– 2, 7) y – 7 = 3(x + 2) Write an equation in slope-intercept form for each line. 3. line with slope – 3 containing (0, 2. 5) y = – 3 x + 2. 5 4. line with slope – 1/2 containing (4, – 6) y = – 1/2 x – 4 5. line through (1, 5) and (3, 11) y = 3 x + 2 6. Standardized Test Practice: Which of the following describes the line y = – 2/3 x + 6? A parallel to the line y = 3/2 x + 6 B perpendicular to the line y = – 3/2 x + 6 C x-intercept is 6; y-intercept is 9 D x-intercept is 9; y-intercept is 6

Objectives • Recognize angle conditions that occur with parallel lines • Prove that two lines are parallel based on given angle relationships

Vocabulary • No new vocabulary words or symbols

t Postulates & Theorems To Prove Lines Parallel k 3 l 5 7 1 2 4 6 8 Postulate/ Theorem Statement Examples Postulate 3. 4 If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel If 1 5 or 2 6 or 3 7 or 4 8, then k || l Parallel Postulate If a given line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line None illustrated Theorem 3. 5 If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel If 1 8 or 2 7, then k || l Theorem 3. 6 If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles are supplementary, then the lines are parallel If m 3 + m 5 = 180° or m 4 + m 6 = 180°, then k || l Theorem 3. 7 If two lines in a plane are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel If 3 6 or 4 5, then k || l

Determine which lines, if any, are parallel. interior angles are supplementary. So, consecutive interior angles are not supplementary. So, c is not parallel to a or b. Answer:

Determine which lines, if any, are parallel. Answer:

ALGEBRA Find x and m ZYN so that Explore From the figure, you know that and You also know that are alternate exterior angles.

Plan For line PQ to be parallel to MN, the alternate exterior angles must be congruent. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find Solve Alternate exterior angles Substitution Subtract 7 x from each side. Add 25 to each side. Divide each side by 4.

Original equation Simplify. Examine Verify the angle measure by using the value of x to find Since Answer:

ALGEBRA Find x and m GBA so that Answer:

Answer:

Answer: Since the slopes are not equal, r is not parallel to s.

Summary & Homework • Summary: – When lines are cut by a transversal, certain angle relationships produce parallel lines • • Congruent corresponding angles Congruent alternate interior angles Congruent alternate exterior angles Supplementary consecutive interior angles • Homework: pg 154 -155: 4, 7, 13 -16, 27, 29, 31