LESSON 3 5 Proving Lines Parallel FiveMinute Check

LESSON 3– 5 Proving Lines Parallel

Five-Minute Check (over Lesson 3– 4) TEKS Then/Now Postulate 3. 4: Converse of Corresponding Angles Postulate 3. 5: Parallel Postulate Theorems: Proving Lines Parallel Example 1: Identify Parallel Lines Example 2: Use Angle Relationships Example 3: Real-World Example: Prove Lines Parallel

Over Lesson 3– 4 containing the point (5, – 2) in point-slope form? A. B. C. D.

Over Lesson 3– 4 What is the equation of the line with slope 3 containing the point (– 2, 7) in point-slope form? A. y = 3 x + 7 B. y = 3 x – 2 C. y – 7 = 3 x + 2 D. y – 7 = 3(x + 2)

Over Lesson 3– 4 What equation represents a line with slope – 3 containing the point (0, 2. 5) in slope-intercept form? A. y = – 3 x + 2. 5 B. y = – 3 x C. y – 2. 5 = – 3 x D. y = – 3(x + 2. 5)

Over Lesson 3– 4 containing the point (4, – 6) in slope-intercept form? A. B. C. D.

Over Lesson 3– 4 What equation represents a line containing points (1, 5) and (3, 11)? A. y = 3 x + 2 B. y = 3 x – 2 C. y – 6 = 3(x – 2) D. y – 6 = 3 x + 2

Over Lesson 3– 4 A. B. C. D.

Targeted TEKS G. 5(B) Construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge. G. 6(A) Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and these relationships to solve problems. Mathematical Processes G. 1(E), G. 1(F)

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. 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.

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.

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 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.

Use Angle Relationships Find m ZYN so that || . Show your work. Read the Item From the figure, you know that m WXP = 11 x – 25 and m ZYN = 7 x + 35. You are asked to find m ZYN.

Use Angle Relationships Solve the 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 11 x – 25 = 7 x + 35 Substitution 4 x – 25 = 35 4 x = 60 x = 15 Subtract 7 x from each side. Add 25 to each side. Divide each side by 4.

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

ALGEBRA Find x so that A. x = 60 B. x = 9 C. x = 12 D. x = 12 || .

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.

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. C. The vertical lines are perpendicular to the horizontal lines. D. All of these statements are true.

LESSON 3– 5 Proving Lines Parallel