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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Sigma Prep · sigmaprep.io/worksheets Name Midsegments and Centroids Date Period Answer each question. Use the midsegment theorem Find the length of the side the midsegment is parallel to. The midsegment $\overline{C G}$ of $△ M J S$ is parallel to $\overline{J S}$ . Given $J S = 24$ , find $C G$ . In $△ T S F$ , $D$ and $W$ are the midpoints of $\overline{T S}$ and $\overline{T F}$ . If $S F = 12$ , find $D W$ . Find $x$ . $\overline{M S}$ joins the midpoints of $\overline{F K}$ and $\overline{F Z}$ in $△ F K Z$ , and $M S = 11$ . How long is $\overline{K Z}$ ? The segment joins the midpoints of two sides. Find $x$ . Points $J$ and $W$ bisect sides $\overline{E D}$ and $\overline{E B}$ of $△ E D B$ . With $D B = 6$ , what is $J W$ ? The midsegment $\overline{V B}$ of $△ W L P$ is parallel to $\overline{L P}$ . Given $V B = 2$ , find $L P$ . How long is the midsegment? Points $C$ and $S$ bisect sides $\overline{A Y}$ and $\overline{A W}$ of $△ A Y W$ . With $C S = 13$ , what is $Y W$ ? Use the centroid formula Find the centroid of the triangle with vertices $(- 4, - 6),$ $(0, - 8),$ $(- 2, 5)$ . Find the centroid of the triangle with vertices $(4, - 9),$ $(- 8, - 9),$ $(- 2, 3)$ . Find the centroid of the triangle with vertices $(1, 7), (7, 2), (4, 3)$ . Find the centroid of the triangle with vertices $(5, - 8),$ $(- 8, 6),$ $(3, 8)$ . Find the centroid of the triangle with vertices $(- 2, 3),$ $(- 7, - 1),$ $(0, - 5)$ . Find the centroid of the triangle with vertices $(9, 9),$ $(- 4, - 3),$ $(- 2, - 6)$ . Find the centroid of the triangle with vertices $(- 6, 0),$ $(7, - 8),$ $(8, - 1)$ . Find the centroid of the triangle with vertices $(- 5, 0),$ $(0, 5),$ $(- 1, - 5)$ . Find the centroid of the triangle with vertices $(10, 4),$ $(- 2, 2),$ $(- 8, - 9)$ . Find the centroid of the triangle with vertices $(8, - 6),$ $(5, 9),$ $(- 1, 6)$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Midsegments and Centroids

Date Period

Answer each question.

Use the midsegment theorem
Find the length of the side the midsegment is parallel to.
The midsegment $\overline{C G}$ of $△ M J S$ is parallel to $\overline{J S}$ . Given $J S = 24$ , find $C G$ .
In $△ T S F$ , $D$ and $W$ are the midpoints of $\overline{T S}$ and $\overline{T F}$ . If $S F = 12$ , find $D W$ .
Find $x$ .
$\overline{M S}$ joins the midpoints of $\overline{F K}$ and $\overline{F Z}$ in $△ F K Z$ , and $M S = 11$ . How long is $\overline{K Z}$ ?
The segment joins the midpoints of two sides. Find $x$ .
Points $J$ and $W$ bisect sides $\overline{E D}$ and $\overline{E B}$ of $△ E D B$ . With $D B = 6$ , what is $J W$ ?
The midsegment $\overline{V B}$ of $△ W L P$ is parallel to $\overline{L P}$ . Given $V B = 2$ , find $L P$ .
How long is the midsegment?
Points $C$ and $S$ bisect sides $\overline{A Y}$ and $\overline{A W}$ of $△ A Y W$ . With $C S = 13$ , what is $Y W$ ?

Use the centroid formula
Find the centroid of the triangle with vertices $(- 4, - 6),$ $(0, - 8),$ $(- 2, 5)$ .
Find the centroid of the triangle with vertices $(4, - 9),$ $(- 8, - 9),$ $(- 2, 3)$ .
Find the centroid of the triangle with vertices $(1, 7), (7, 2), (4, 3)$ .
Find the centroid of the triangle with vertices $(5, - 8),$ $(- 8, 6),$ $(3, 8)$ .
Find the centroid of the triangle with vertices $(- 2, 3),$ $(- 7, - 1),$ $(0, - 5)$ .
Find the centroid of the triangle with vertices $(9, 9),$ $(- 4, - 3),$ $(- 2, - 6)$ .
Find the centroid of the triangle with vertices $(- 6, 0),$ $(7, - 8),$ $(8, - 1)$ .
Find the centroid of the triangle with vertices $(- 5, 0),$ $(0, 5),$ $(- 1, - 5)$ .
Find the centroid of the triangle with vertices $(10, 4),$ $(- 2, 2),$ $(- 8, - 9)$ .
Find the centroid of the triangle with vertices $(8, - 6),$ $(5, 9),$ $(- 1, 6)$ .



Sigma Prep · sigmaprep.io/worksheets Name Midsegments and CentroidsAnswer keyVersion 1 Date Period Answer each question. Use the midsegment theorem Find the length of the side the midsegment is parallel to. $18$ The midsegment $\overline{C G}$ of $△ M J S$ is parallel to $\overline{J S}$ . Given $J S = 24$ , find $C G$ . $12$ In $△ T S F$ , $D$ and $W$ are the midpoints of $\overline{T S}$ and $\overline{T F}$ . If $S F = 12$ , find $D W$ . $6$ Find $x$ . $5$ $\overline{M S}$ joins the midpoints of $\overline{F K}$ and $\overline{F Z}$ in $△ F K Z$ , and $M S = 11$ . How long is $\overline{K Z}$ ? $22$ The segment joins the midpoints of two sides. Find $x$ . $14$ Points $J$ and $W$ bisect sides $\overline{E D}$ and $\overline{E B}$ of $△ E D B$ . With $D B = 6$ , what is $J W$ ? $3$ The midsegment $\overline{V B}$ of $△ W L P$ is parallel to $\overline{L P}$ . Given $V B = 2$ , find $L P$ . $4$ How long is the midsegment? $8$ Points $C$ and $S$ bisect sides $\overline{A Y}$ and $\overline{A W}$ of $△ A Y W$ . With $C S = 13$ , what is $Y W$ ? $26$ Use the centroid formula Find the centroid of the triangle with vertices $(- 4, - 6),$ $(0, - 8),$ $(- 2, 5)$ . $(- 2, - 3)$ Find the centroid of the triangle with vertices $(4, - 9),$ $(- 8, - 9),$ $(- 2, 3)$ . $(- 2, - 5)$ Find the centroid of the triangle with vertices $(1, 7), (7, 2), (4, 3)$ . $(4, 4)$ Find the centroid of the triangle with vertices $(5, - 8),$ $(- 8, 6),$ $(3, 8)$ . $(0, 2)$ Find the centroid of the triangle with vertices $(- 2, 3),$ $(- 7, - 1),$ $(0, - 5)$ . $(- 3, - 1)$ Find the centroid of the triangle with vertices $(9, 9),$ $(- 4, - 3),$ $(- 2, - 6)$ . $(1, 0)$ Find the centroid of the triangle with vertices $(- 6, 0),$ $(7, - 8),$ $(8, - 1)$ . $(3, - 3)$ Find the centroid of the triangle with vertices $(- 5, 0),$ $(0, 5),$ $(- 1, - 5)$ . $(- 2, 0)$ Find the centroid of the triangle with vertices $(10, 4),$ $(- 2, 2),$ $(- 8, - 9)$ . $(0, - 1)$ Find the centroid of the triangle with vertices $(8, - 6),$ $(5, 9),$ $(- 1, 6)$ . $(4, 3)$ 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.

Use the midsegment theorem
Find the length of the side the midsegment is parallel to. $18$
The midsegment $\overline{C G}$ of $△ M J S$ is parallel to $\overline{J S}$ . Given $J S = 24$ , find $C G$ . $12$
In $△ T S F$ , $D$ and $W$ are the midpoints of $\overline{T S}$ and $\overline{T F}$ . If $S F = 12$ , find $D W$ . $6$
Find $x$ . $5$
$\overline{M S}$ joins the midpoints of $\overline{F K}$ and $\overline{F Z}$ in $△ F K Z$ , and $M S = 11$ . How long is $\overline{K Z}$ ? $22$
The segment joins the midpoints of two sides. Find $x$ . $14$
Points $J$ and $W$ bisect sides $\overline{E D}$ and $\overline{E B}$ of $△ E D B$ . With $D B = 6$ , what is $J W$ ? $3$
The midsegment $\overline{V B}$ of $△ W L P$ is parallel to $\overline{L P}$ . Given $V B = 2$ , find $L P$ . $4$
How long is the midsegment? $8$
Points $C$ and $S$ bisect sides $\overline{A Y}$ and $\overline{A W}$ of $△ A Y W$ . With $C S = 13$ , what is $Y W$ ? $26$

Use the centroid formula
Find the centroid of the triangle with vertices $(- 4, - 6),$ $(0, - 8),$ $(- 2, 5)$ . $(- 2, - 3)$
Find the centroid of the triangle with vertices $(4, - 9),$ $(- 8, - 9),$ $(- 2, 3)$ . $(- 2, - 5)$
Find the centroid of the triangle with vertices $(1, 7), (7, 2), (4, 3)$ . $(4, 4)$
Find the centroid of the triangle with vertices $(5, - 8),$ $(- 8, 6),$ $(3, 8)$ . $(0, 2)$
Find the centroid of the triangle with vertices $(- 2, 3),$ $(- 7, - 1),$ $(0, - 5)$ . $(- 3, - 1)$
Find the centroid of the triangle with vertices $(9, 9),$ $(- 4, - 3),$ $(- 2, - 6)$ . $(1, 0)$
Find the centroid of the triangle with vertices $(- 6, 0),$ $(7, - 8),$ $(8, - 1)$ . $(3, - 3)$
Find the centroid of the triangle with vertices $(- 5, 0),$ $(0, 5),$ $(- 1, - 5)$ . $(- 2, 0)$
Find the centroid of the triangle with vertices $(10, 4),$ $(- 2, 2),$ $(- 8, - 9)$ . $(0, - 1)$
Find the centroid of the triangle with vertices $(8, - 6),$ $(5, 9),$ $(- 1, 6)$ . $(4, 3)$

How to do these

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

A midsegment is half its parallel side.
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 medians.

What you can put on this worksheet

Midsegments, both directions: Find $x$ . — a triangle with its midsegment drawn, labeled 16 → $8$
The centroid from three vertices: Find the centroid of the triangle with vertices $(- 2, 7),$ $(1, 6),$ $(- 5, 2)$ . → $(- 2, 5)$
Midsegments written in x: Solve for $x$ . — triangle jkl with midsegment st, labeled J, K, L, S, T, 24 → $8$
The 2 : 1 ratio on a median: G is the centroid and $G Z = 7$ . Find $C G$ . — a triangle with its three medians meeting at the centroid, labeled A, B, C, Z, G, ?, 7 → $14$

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 4: midsegments, both directions, the centroid from three vertices, midsegments written in x and the 2 : 1 ratio on a median. 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.

Midsegment and centroid worksheet

Select your difficulty

Use the midsegment theorem

Use the centroid formula

Use the midsegment theorem

Use the centroid formula

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these midsegment and centroid worksheets free?+

Do the midsegment and centroid worksheets come with an answer key?+

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What grade are these midsegment and centroid worksheets for?+

Can I get a different version of the same midsegment and centroid worksheet?+

Is this a free alternative to Kuta Software for midsegment and centroid?+

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What kinds of question are on a midsegment and centroid worksheet?+

What do students get wrong with midsegment and centroid?+