Worksheets · Geometry

Parallel and perpendicular lines worksheet for Geometry

In Geometry slopes are how you tell whether two lines on the coordinate plane are parallel or perpendicular: compare slopes, classify a pair of lines from equations or points, and write the equation of a parallel or perpendicular line through a given point.

Also taught in Algebra 1, at its own level and with its own examples.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Parallel and Perpendicular Lines

Date Period

Answer each question.

  1. Find parallel and perpendicular slopes

    Find the slope of a line parallel to y=2x+11
  2. Find the slope of a line perpendicular to y=3x+3
  3. Find the slope of a line parallel to y=x+11
  4. Find the slope of a line perpendicular to y=2x−11
  5. Find the slope of a line parallel to y=−5x−9

  1. Write a parallel or perpendicular line

    Write the equation of the line through (−7,6) perpendicular to y=−72x−8, in slope-intercept form.
  2. Write the equation of the line through (4,−8) parallel to y=−72x−1, in slope-intercept form.
  3. Write the equation of the line through (21,7) perpendicular to y=−73x+5, in slope-intercept form.
  4. Write the equation of the line through (−4,−3) parallel to y=14x+8, in slope-intercept form.
  5. Write the equation of the line through (8,3) perpendicular to y=−83x−2, in slope-intercept form.

  1. Classify lines: parallel, perpendicular or neither

    Parallel, perpendicular or neither? y=34x+3 and y=34x−2
  2. Parallel, perpendicular or neither? y=−32x+8 and y=−32x
  3. Parallel, perpendicular or neither? y=23x−8 and y=−32x+8
  4. Parallel, perpendicular or neither? y=−x−5 and y=−x+4
  5. Parallel, perpendicular or neither? y=34x−8 and y=14x+3

  1. Compare two lines through given points

    Line 1 passes through (−6,−5) and (−4,−6); line 2 through (−4,−6) and (−2,−6). Parallel, perpendicular or neither?
  2. Line 1 passes through (4,5) and (9,7); line 2 through (4,−1) and (14,3). Parallel, perpendicular or neither?
  3. Line 1 passes through (5,5) and (9,2); line 2 through (−1,−4) and (7,−10). Parallel, perpendicular or neither?
  4. Line 1 passes through (1,6) and (6,8); line 2 through (−6,1) and (−1,4). Parallel, perpendicular or neither?
  5. Line 1 passes through (1,−4) and (2,−3); line 2 through (−1,−2) and (0,0). Parallel, perpendicular or neither?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Parallel and Perpendicular LinesAnswer keyVersion 2

Date Period

Answer each question.

  1. Find parallel and perpendicular slopes

    Find the slope of a line parallel to y=2x+112
  2. Find the slope of a line perpendicular to y=3x+3−13
  3. Find the slope of a line parallel to y=x+111
  4. Find the slope of a line perpendicular to y=2x−11−12
  5. Find the slope of a line parallel to y=−5x−9−5

  1. Write a parallel or perpendicular line

    Write the equation of the line through (−7,6) perpendicular to y=−72x−8, in slope-intercept form.y=27x+8
  2. Write the equation of the line through (4,−8) parallel to y=−72x−1, in slope-intercept form.y=−72x+6
  3. Write the equation of the line through (21,7) perpendicular to y=−73x+5, in slope-intercept form.y=37x−2
  4. Write the equation of the line through (−4,−3) parallel to y=14x+8, in slope-intercept form.y=14x−2
  5. Write the equation of the line through (8,3) perpendicular to y=−83x−2, in slope-intercept form.y=38x

  1. Classify lines: parallel, perpendicular or neither

    Parallel, perpendicular or neither? y=34x+3 and y=34x−2Parallel
  2. Parallel, perpendicular or neither? y=−32x+8 and y=−32xParallel
  3. Parallel, perpendicular or neither? y=23x−8 and y=−32x+8Perpendicular
  4. Parallel, perpendicular or neither? y=−x−5 and y=−x+4Parallel
  5. Parallel, perpendicular or neither? y=34x−8 and y=14x+3Neither

  1. Compare two lines through given points

    Line 1 passes through (−6,−5) and (−4,−6); line 2 through (−4,−6) and (−2,−6). Parallel, perpendicular or neither?Neither
  2. Line 1 passes through (4,5) and (9,7); line 2 through (4,−1) and (14,3). Parallel, perpendicular or neither?Parallel
  3. Line 1 passes through (5,5) and (9,2); line 2 through (−1,−4) and (7,−10). Parallel, perpendicular or neither?Parallel
  4. Line 1 passes through (1,6) and (6,8); line 2 through (−6,1) and (−1,4). Parallel, perpendicular or neither?Neither
  5. Line 1 passes through (1,−4) and (2,−3); line 2 through (−1,−2) and (0,0). Parallel, perpendicular or neither?Neither

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Write the equation of the line through (4,1) perpendicular to y=2x−3

  1. A perpendicular slope is the negative reciprocal: the slope 2 becomes -1/2.
  2. Put (4, 1) into y = -1/2 x + b: 1 = -2 + b, so b = 3.

The answer is y=−12x+3.

Where students go wrong

Taking only half of the negative reciprocal. Perpendicular to slope 2 is -1/2: flipping to 1/2 without changing the sign, or changing the sign to -2 without flipping, gives a line that is not perpendicular.

Also called negative reciprocal, slopes of parallel lines or perpendicular slope.

What you can put on this worksheet

Slopes of parallel and perpendicular lines
Find the slope of a line parallel to y=3x−6 → 3
The equation through a point, parallel or perpendicular
Write the equation of the line through (0,−4) perpendicular to y=3x+1, in slope-intercept form. → y=−13x−4
Parallel, perpendicular or neither
Parallel, perpendicular or neither? y=34x+4 and y=−43x−7 → Perpendicular
Two lines through two points each: parallel, perpendicular or neither
Line 1 passes through (−5,0) and (−1,−3); line 2 through (1,−3) and (−2,−7). Parallel, perpendicular or neither? → Perpendicular
Read the slope off the picture
The dashed lines show the rise and the run between the two marked points. Find the slope of the line. → 3
Slope of a horizontal or vertical line, from a graph
Find the slope of the line. → 0
Slope of a horizontal or vertical line, from its equation
Find the slope of y=7. → 0

Questions about these worksheets

Yes. Every parallel and perpendicular lines sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the parallel and perpendicular lines questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 7: slopes of parallel and perpendicular lines, the equation through a point, parallel or perpendicular, parallel, perpendicular or neither, two lines through two points each: parallel, perpendicular or neither, read the slope off the picture, slope of a horizontal or vertical line, from a graph and slope of a horizontal or vertical line, from its equation. Tick as many as you want and set how many of each, or let it spread them evenly.

Flipping without negating, or negating without flipping. Both are needed, and the check is that the two slopes multiply to exactly -1.