Midsegment of a triangle worksheet

Join the midpoints of two sides and the segment you get is parallel to the third side and exactly half its length. That works in both directions, which is what the questions swap between.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Midsegments of Triangles Date Period Answer each question. Use the midsegment theorem Find the length of the side the midsegment is parallel to. Find $x$ . $\overline{J G}$ joins the midpoints of $\overline{F Z}$ and $\overline{F S}$ in $△ F Z S$ , and $Z S = 10$ . How long is $\overline{J G}$ ? Find the value of $x$ . Find the length of the midsegment. Solve for $x$ . In $△ Y W H$ , $U$ and $C$ are the midpoints of $\overline{Y W}$ and $\overline{Y H}$ . If $U C = 8$ , find $W H$ . Solve for $x$ . The midsegment $\overline{U W}$ of $△ M N K$ is parallel to $\overline{N K}$ . Given $N K = 24$ , find $U W$ . Find the value of $x$ . Find midsegments on the coordinate plane In $△ A B C$ with $A (10, - 4)$ , $B (6, - 6)$ , $C (- 2, 0)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . In $△ A B C$ with $A (- 2, - 8)$ , $B (10, - 8)$ , $C (- 8, 8)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . In $△ A B C$ with $A (2, 2)$ , $B (4, - 8)$ , $C (- 8, 2)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . In $△ A B C$ with $A (0, 0)$ , $B (- 6, - 6)$ , $C (- 4, 10)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . In $△ A B C$ with $A (0, 2)$ , $B (10, 6)$ , $C (6, 10)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . Use midpoints to find lengths $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 4 x + 3$ and $D B = x + 18$ . Find $A B$ . $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 4 x + 4$ and $D B = 5 x - 1$ . Find $A B$ . $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 2 x - 4$ and $D B = x + 5$ . Find $A B$ . $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 6 x - 12$ and $D B = 3 x + 3$ . Find $A B$ . $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = x + 14$ and $D B = 3 x + 2$ . Find $A B$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Midsegments of Triangles

Date Period

Answer each question.

Use the midsegment theorem
Find the length of the side the midsegment is parallel to.
Find $x$ .
$\overline{J G}$ joins the midpoints of $\overline{F Z}$ and $\overline{F S}$ in $△ F Z S$ , and $Z S = 10$ . How long is $\overline{J G}$ ?
Find the value of $x$ .
Find the length of the midsegment.
Solve for $x$ .
In $△ Y W H$ , $U$ and $C$ are the midpoints of $\overline{Y W}$ and $\overline{Y H}$ . If $U C = 8$ , find $W H$ .
Solve for $x$ .
The midsegment $\overline{U W}$ of $△ M N K$ is parallel to $\overline{N K}$ . Given $N K = 24$ , find $U W$ .
Find the value of $x$ .

Find midsegments on the coordinate plane
In $△ A B C$ with $A (10, - 4)$ , $B (6, - 6)$ , $C (- 2, 0)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ .
In $△ A B C$ with $A (- 2, - 8)$ , $B (10, - 8)$ , $C (- 8, 8)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ .
In $△ A B C$ with $A (2, 2)$ , $B (4, - 8)$ , $C (- 8, 2)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ .
In $△ A B C$ with $A (0, 0)$ , $B (- 6, - 6)$ , $C (- 4, 10)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ .
In $△ A B C$ with $A (0, 2)$ , $B (10, 6)$ , $C (6, 10)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ .

Use midpoints to find lengths
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 4 x + 3$ and $D B = x + 18$ . Find $A B$ .
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 4 x + 4$ and $D B = 5 x - 1$ . Find $A B$ .
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 2 x - 4$ and $D B = x + 5$ . Find $A B$ .
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 6 x - 12$ and $D B = 3 x + 3$ . Find $A B$ .
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = x + 14$ and $D B = 3 x + 2$ . Find $A B$ .



Sigma Prep · sigmaprep.io/worksheets Name Midsegments of TrianglesAnswer keyVersion 1 Date Period Answer each question. Use the midsegment theorem Find the length of the side the midsegment is parallel to. $18$ Find $x$ . $10$ $\overline{J G}$ joins the midpoints of $\overline{F Z}$ and $\overline{F S}$ in $△ F Z S$ , and $Z S = 10$ . How long is $\overline{J G}$ ? $5$ Find the value of $x$ . $15$ Find the length of the midsegment. $4$ Solve for $x$ . $9$ In $△ Y W H$ , $U$ and $C$ are the midpoints of $\overline{Y W}$ and $\overline{Y H}$ . If $U C = 8$ , find $W H$ . $16$ Solve for $x$ . $11$ The midsegment $\overline{U W}$ of $△ M N K$ is parallel to $\overline{N K}$ . Given $N K = 24$ , find $U W$ . $12$ Find the value of $x$ . $13$ Find midsegments on the coordinate plane In $△ A B C$ with $A (10, - 4)$ , $B (6, - 6)$ , $C (- 2, 0)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (8, - 5)$ , $N (4, - 2)$ In $△ A B C$ with $A (- 2, - 8)$ , $B (10, - 8)$ , $C (- 8, 8)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (4, - 8)$ , $N (- 5, 0)$ In $△ A B C$ with $A (2, 2)$ , $B (4, - 8)$ , $C (- 8, 2)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (3, - 3)$ , $N (- 3, 2)$ In $△ A B C$ with $A (0, 0)$ , $B (- 6, - 6)$ , $C (- 4, 10)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (- 3, - 3)$ , $N (- 2, 5)$ In $△ A B C$ with $A (0, 2)$ , $B (10, 6)$ , $C (6, 10)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (5, 4)$ , $N (3, 6)$ Use midpoints to find lengths $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 4 x + 3$ and $D B = x + 18$ . Find $A B$ . $46$ $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 4 x + 4$ and $D B = 5 x - 1$ . Find $A B$ . $48$ $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 2 x - 4$ and $D B = x + 5$ . Find $A B$ . $28$ $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 6 x - 12$ and $D B = 3 x + 3$ . Find $A B$ . $36$ $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = x + 14$ and $D B = 3 x + 2$ . Find $A B$ . $40$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Midsegments of TrianglesAnswer keyVersion 1

Date Period

Answer each question.

Use the midsegment theorem
Find the length of the side the midsegment is parallel to. $18$
Find $x$ . $10$
$\overline{J G}$ joins the midpoints of $\overline{F Z}$ and $\overline{F S}$ in $△ F Z S$ , and $Z S = 10$ . How long is $\overline{J G}$ ? $5$
Find the value of $x$ . $15$
Find the length of the midsegment. $4$
Solve for $x$ . $9$
In $△ Y W H$ , $U$ and $C$ are the midpoints of $\overline{Y W}$ and $\overline{Y H}$ . If $U C = 8$ , find $W H$ . $16$
Solve for $x$ . $11$
The midsegment $\overline{U W}$ of $△ M N K$ is parallel to $\overline{N K}$ . Given $N K = 24$ , find $U W$ . $12$
Find the value of $x$ . $13$

Find midsegments on the coordinate plane
In $△ A B C$ with $A (10, - 4)$ , $B (6, - 6)$ , $C (- 2, 0)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (8, - 5)$ , $N (4, - 2)$
In $△ A B C$ with $A (- 2, - 8)$ , $B (10, - 8)$ , $C (- 8, 8)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (4, - 8)$ , $N (- 5, 0)$
In $△ A B C$ with $A (2, 2)$ , $B (4, - 8)$ , $C (- 8, 2)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (3, - 3)$ , $N (- 3, 2)$
In $△ A B C$ with $A (0, 0)$ , $B (- 6, - 6)$ , $C (- 4, 10)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (- 3, - 3)$ , $N (- 2, 5)$
In $△ A B C$ with $A (0, 2)$ , $B (10, 6)$ , $C (6, 10)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . $M (5, 4)$ , $N (3, 6)$

Use midpoints to find lengths
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 4 x + 3$ and $D B = x + 18$ . Find $A B$ . $46$
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 4 x + 4$ and $D B = 5 x - 1$ . Find $A B$ . $48$
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 2 x - 4$ and $D B = x + 5$ . Find $A B$ . $28$
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = 6 x - 12$ and $D B = 3 x + 3$ . Find $A B$ . $36$
$D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = x + 14$ and $D B = 3 x + 2$ . Find $A B$ . $40$

How to do these

The third side is $18$

The midsegment is half of it.
Half of 18.
So the midsegment is 9.

The answer is $9$ .

Where students go wrong

Halving the wrong one. The midsegment is the short one and the side it is parallel to is the long one, so going from the midsegment back to the side means doubling, not halving.

Also called midsegment theorem or midline of a triangle.

What you can put on this worksheet

Midsegments, both directions: Find $x$ . — a triangle with its midsegment drawn, labeled 16 → $8$
Midsegments written in x: Solve for $x$ . — triangle jkl with midsegment st, labeled J, K, L, S, T, 24 → $8$
On the coordinate plane: In $△ A B C$ with $A (- 4, 10)$ , $B (- 2, 8)$ , $C (2, 10)$ , $M$ is the midpoint of $\overline{A B}$ and $N$ is the midpoint of $\overline{A C}$ . Find $M$ and $N$ . → $M (- 3, 9)$ , $N (- 1, 10)$
The halves of a side, in x: $D$ is the midpoint of $\overline{A B}$ , $E$ the midpoint of $\overline{A C}$ . $A D = x + 15$ and $D B = 3 x - 3$ . Find $A B$ . → $48$
Which side it is parallel to, extra lengths, halves in x: Find $x$ . — a triangle with its midpoints and midsegments, labeled x, 18, 12 → $24$

Questions about these worksheets

Yes. Every midsegment of a triangle 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 of a triangle 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 5: midsegments, both directions, midsegments written in x, on the coordinate plane, the halves of a side, in x and which side it is parallel to, extra lengths, halves in x. Tick as many as you want and set how many of each, or let it spread them evenly.

Halving the wrong one. The midsegment is the short one and the side it is parallel to is the long one, so going from the midsegment back to the side means doubling, not halving.

Midsegment of a triangle worksheet

Select your difficulty

Use the midsegment theorem

Find midsegments on the coordinate plane

Use midpoints to find lengths

Use the midsegment theorem

Find midsegments on the coordinate plane

Use midpoints to find lengths

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these midsegment of a triangle worksheets free?+

Do the midsegment of a triangle worksheets come with an answer key?+

Are these midsegment of a triangle worksheets printable?+

What grade are these midsegment of a triangle worksheets for?+

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

Is this a free alternative to Kuta Software for midsegment of a triangle?+

Can I choose how hard the midsegment of a triangle questions are?+

What kinds of question are on a midsegment of a triangle worksheet?+

What do students get wrong with midsegment of a triangle?+