Grade 10 · Math · Geometry

10th grade Midsegments of triangles worksheet

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Midsegments of triangles

Grade 10 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

Kira walks in a triangular park. Its three midsegments form △QSU, with sides 13, 17 and 20 m. What is the perimeter of △DFG, in m?
Luz studies three towns on a map. Its three midsegments form △UYQ, with sides 21, 28 and 35 miles. What is the perimeter of △CHW, in miles?
Milo looks at a triangular sail. Its three midsegments form △DHW, with sides 5, 7 and 9 feet. What is the perimeter of △SGV, in feet?
Noah folds a paper triangle. Its three midsegments form △CYG, with sides 8, 11 and 12 cm. What is the perimeter of △FQU, in cm?
Ren looks at the triangular front of a tent. WY = (2x + 1) feet, CU = (3x + 6) feet and WQ = (3x + 2) feet. How long is HU, in feet?
Tala cuts a triangular slice of pizza. GD = (3x − 2) cm, SV = (5x + 2) cm and GF = (x + 7) cm. How long is QV, in cm?
Zee walks in a triangular park. YC = (x + 8) m, WH = (4x − 14) m and YG = (2x − 9) m. How long is UH, in m?
Bo looks at the triangular front of a tent. The crossbar UY joins two midpoints, m∠CUY = (2x + 15)° and m∠CWH = (4x − 21)°. What is m∠WUY, in degrees?
Esme looks at the brace under a ramp. The bar SF joins two midpoints, m∠GSF = (6x − 8)° and m∠GVQ = (4x + 20)°. What is m∠VSF, in degrees?
Jun cuts a triangular wedge of cheese. The cut CH joins two midpoints, m∠WCH = (5x − 7)° and m∠WUD = (2x + 23)°. What is m∠UCH, in degrees?

Midsegments of triangles. Every version has 10 questions, and the answer key prints on the second page.

I can say that a midsegment is parallel to the third side and half as long, and use it both ways.
I can find the perimeter of the triangle made by the three midsegments, or the big triangle's perimeter from it.
I can write 2 × midsegment = third side, solve for x, and use the parallel to find angles.

Standard: G-CO.C.10

midpoint: The point that cuts a segment into two equal halves.

midsegment: A segment joining the midpoints of two sides of a triangle.

third side: The side the midsegment never touches; the midsegment runs beside it.

parallel (∥): Running the same way and never meeting.

tick marks, arrows: Marks on a sketch: same ticks mean equal lengths; arrows mean parallel lines.

Your child doubled when the midsegment is half.

Your child gave the length of the third side, not the midsegment.

Your child halved one of the sides the midpoints sit on.

Ask: is the segment across the middle longer or shorter than the side it runs beside?

Ask: which segment does the question ask for?

Ask: which side does the midsegment run beside without touching?

What is the most common mistake with midsegments of triangles?

Your child doubled when the midsegment is half.

How can I help my child with midsegments of triangles?

Ask: is the segment across the middle longer or shorter than the side it runs beside?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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