$100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are Parallel
Parallel Lines and Transversals for $100 Define: Skew lines
Answer Skew Lines - Lines that are not coplanar and do not intersect Back
Parallel Lines and Transversals for $200 Define: Parallel Lines
Answer Parallel Lines – Lines that are coplanar and do not intersect. Back
Parallel Lines and Transversals for $300 Define: Transversal
Answer Transversal – A line that intersects two or more lines in a plane at different points Back
Parallel Lines and Transversals for $400 Name all the line segments parallel to AB
Answer Back CD, GH, EF
Parallel Lines and Transversals for $500 Name all of the line segments perpendicular to GC
Answer Back EG, GH, CA, CD
Angles and Parallel Lines for $100 Identify two pairs of consecutive interior angles in the following drawing given l || m: l m n
Answer <4 and <5, <3 and <6 Note: <4 + <5 = 180 degrees Back l m n
Angles and Parallel Lines for $200 Identify two pairs of corresponding angles in the following drawing given l || m: l m n
Answer 1 and 5, 4 and 8, 2 and 6, 3 and 7 NOTE: 1 5 Back l m n
Angles and Parallel Lines for $300 Identify two pairs of alternate interior angles in the following drawing given l || m: l m n
Answer <4 and <6, <3 and <5 Note: <4 <6 Back l m n
Angles and Parallel Lines for $400 Given r is parallel to t, find the measure of angle 6
Answer Back <2 = 135 degree angle – corresponding angles. <2 and < 6 are supplementary < 6 = 180 <6 = 45 degrees
Angles and Parallel Lines for $500 m<1 = 6x, and m<3 = 7x Find the value of x for p to be parallel to q. The diagram is not to scale.
Answer Back m<1 must be congruent to m<3 for p || q 6x = 7x – = x
Equations of Lines for $100 Write the equation of the line in slope-intercept form: The line with a slope of -5 through point (-2, -4)
Answer Point: (-2, -4) m = -5 Slope-intercept Form: y = mx + b -4 = -5(-2) + b -4 = 10 + b -14 = b Thus, y = -5x - 14 Back
Equations of Lines for $200 Write the equation of the line in slope-intercept form: The line through points (-2, 3) and (0, -1)
Answer Point: (-2, 3) Point: (0, -1) m = (y 2 – y 1 )/(x 2 – x 1 ) m = (-1- 3)/(0 – -2) = -4/2 = -2 Slope-intercept Form: y = mx + b -1 = -2(0) + b -1 = b Thus, y = -2x - 1 Back
Equations of Lines for $300 Write the equation of the line in point-slope form: The line through points (2, -3) and (-2, 3)
Answer Points: (2, -3) and (-2, 3) m = (y 2 – y 1 )/(x 2 – x 1 ) m = (3- -3)/(-2 – 2) = 6/-4 = -3/2 Point-Slope Form: y – y 1 = m(x – x 1 ) where (x 1, y 1 ) is a point on the line Thus, the equation of the line is y – 3 = -3/2(x - -2) y – 3 = -3/2(x + 2) Back
Equations of Lines for $400 Write the equation of a line perpendicular to the given line that intersects the given line on the y-axis. Write your answer in point-slope form: y = 3x - 8
Answer y = 3x – 8 So, m = 3, a point on the line = (0,-8) Point-Slope Form: y – y 1 = m(x – x 1 ) y - -8 = 3(x – 0) y + 8 = 3x Slope of the Perpendicular line: (-1/3) y + 8 = (-1/3)x Back
Equations of Lines for $500 Graph the following line: y = 3x - 2
Answer 3x - 2 Back
Proving Lines to be Parallel for $100 Which 2 lines are parallel? a) 5y = -3x - 5 b) 5y = -1 – 3x c) 3y – 2x = -1
Answer Back Writing the lines in slope-intercept form: a) 5y = -3x – 5 y = (-3/5)x – 1 b) 5y = -1 – 3x y = (-3/5)x – (1/5) c) 3y – 2x = -1 3y = 2x – 1 y = (2/3)x – (1/3) a||b
Proving Lines to be Parallel for $200 Given: <3 is supplemental to <8 Prove: p || r
Answer Back StatementsReasons <3 is supplemental to <8Given <3 + <8 = 180Def. of Supplemental angles <3 + <4 = 180Def of Supplementary angles <4 is congruent to <8Theorem: Two angles supplementary to the same angle are congruent <4 and <8 are corresponding angles Definition of corresponding angles p || rTheorem: If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
Proving Lines to be Parallel for $300 Given: <1 is congruent to <5 Prove: p || r
Answer Back StatementsReasons <1 is congruent to <5 Given <4 is congruent to <1 Vertical Angles <4 <1 and <1 <5 thus, <4 <5 Transitive property of angle congruence Thus, p || r Theorem: If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel
Proving Lines to be Parallel for $400 Suppose you have four pieces of wood like those shown below. If b = 40 degrees can you construct a frame with opposite sides parallel? Explain.
Answer Back No, they are different transversals, so there is no theorem to prove the sides are congruent
Proving Lines to be Parallel for $500 Write a paragraph proof of this theorem: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Given: r is perpendicular to s, t is perpendicular to s Prove: r || t
Answer By the definition of perpendicular, r ┴ s implies m<2 = 90, and t ┴ s implies m<6 = 90. Line s is a transversal. <2 and <6 are corresponding angles. By the Converse of the Corresponding Angles Postulate, r || t. Back
Distance for $100 Define: Distance between lines
Answer Distance between lines: the shortest distance between the two lines Back
Distance for $200 Given that two lines are equidistance from a third line, what can you conclude?
Answer The two lines are parallel to each other Back
Distance for $300 Define: equidistant
Answer Equidistant: The distance between two lines measured along a perpendicular line to the lines is always the same. Back
Distance for $400 What are the steps to find the distance between two parallel lines?
Answer Back 1)Write both lines in slope-intercept form 2)Find the equation of a line perpendicular to the two parallel lines 3)Find the intersection of the perpendicular line with each of the given two lines 4)Find the distance between the two points
Distance for $500 Find the distance between the given parallel lines y = 2x – 3 2x – y = -4
Answer Back d = √(9.8) (See Homework Solution Online)