Worksheets · Geometry

Midsegment and centroid worksheet

A midsegment joins two midpoints and comes out half the length of the side it is parallel to. The centroid, where the medians meet, is simply the average of the three vertices.

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Midsegments and Centroids

Date Period

Answer each question.

  1. Find the side the midsegment is parallel to25x
  2. Find the centroid of the triangle with vertices (1,9),(9,−4),(2,4)
  3. Find the midsegmentx44
  4. Find the centroid of the triangle with vertices (0,0),(−7,−2),(−5,−7)
  5. Find the side the midsegment is parallel to23x
  6. Find the centroid of the triangle with vertices (−2,7),(−4,−6),(−9,−1)
  7. Find the midsegmentx50
  8. Find the centroid of the triangle with vertices (−2,−4),(3,1),(5,−6)
  9. Find the side the midsegment is parallel to27x
  10. Find the centroid of the triangle with vertices (6,10),(−5,5),(−7,−3)
  11. Find the side the midsegment is parallel to21x
  12. Find the centroid of the triangle with vertices (−6,4),(1,−7),(−4,−9)
  13. Find the midsegmentx36
  14. Find the centroid of the triangle with vertices (4,−2),(−4,3),(9,8)
  15. Find the midsegmentx54
  16. Find the centroid of the triangle with vertices (6,10),(−7,−9),(7,−4)
  17. Find the midsegmentx60
  18. Find the centroid of the triangle with vertices (9,4),(−6,3),(9,−7)
  19. Find the side the midsegment is parallel to32x
  20. Find the centroid of the triangle with vertices (−1,−6),(−2,−3),(3,0)

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

Sigma Prep · sigmaprep.io/worksheets

Name

Midsegments and CentroidsAnswer keyVersion 1

Date Period

Answer each question.

  1. Find the side the midsegment is parallel to25x50
  2. Find the centroid of the triangle with vertices (1,9),(9,−4),(2,4)(4,3)
  3. Find the midsegmentx4422
  4. Find the centroid of the triangle with vertices (0,0),(−7,−2),(−5,−7)(−4,−3)
  5. Find the side the midsegment is parallel to23x46
  6. Find the centroid of the triangle with vertices (−2,7),(−4,−6),(−9,−1)(−5,0)
  7. Find the midsegmentx5025
  8. Find the centroid of the triangle with vertices (−2,−4),(3,1),(5,−6)(2,−3)
  9. Find the side the midsegment is parallel to27x54
  10. Find the centroid of the triangle with vertices (6,10),(−5,5),(−7,−3)(−2,4)
  11. Find the side the midsegment is parallel to21x42
  12. Find the centroid of the triangle with vertices (−6,4),(1,−7),(−4,−9)(−3,−4)
  13. Find the midsegmentx3618
  14. Find the centroid of the triangle with vertices (4,−2),(−4,3),(9,8)(3,3)
  15. Find the midsegmentx5427
  16. Find the centroid of the triangle with vertices (6,10),(−7,−9),(7,−4)(2,−1)
  17. Find the midsegmentx6030
  18. Find the centroid of the triangle with vertices (9,4),(−6,3),(9,−7)(4,0)
  19. Find the side the midsegment is parallel to32x64
  20. Find the centroid of the triangle with vertices (−1,−6),(−2,−3),(3,0)(0,−3)

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

How to do these

A midsegment of a triangle is 9. Find the side it is parallel to

  1. A midsegment is half its parallel side.
  2. So the side is twice the midsegment.

The answer is 18.

Where students go wrong

Halving when you should double. The midsegment is the shorter one, always, so if your answer is smaller than what you were given you have gone the wrong way.

Also called midsegment theorem, centroid of a triangle or medians.

What you can put on this worksheet

Midsegments, both directions
Find the midsegment → 8
The centroid from three vertices
Find the centroid of the triangle with vertices (0,2),(3,−5),(−3,6) → (0,1)

Questions about these worksheets

Yes. Every midsegment and centroid 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 midsegment and centroid 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 2: midsegments, both directions and the centroid from three vertices. Tick as many as you want and set how many of each, or let it spread them evenly.

Halving when you should double. The midsegment is the shorter one, always, so if your answer is smaller than what you were given you have gone the wrong way.