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Geometry practice

Triangle Medians Worksheets

Use midpoint facts and the centroid’s 2:1 ratio to find missing lengths, with integer, decimal and algebraic-expression practice.

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Use the drawn medians and centroid C to find each requested length. In algebraic mode, solve for x first.

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Use midpoint and centroid relationships

A median joins a vertex to the midpoint of the opposite side. The three medians meet at centroid C.

Learning objective

What this activity builds

Distinguish equal side halves from the centroid’s unequal division of a median.

Worked example

A median is 24 units long. How far is its vertex from the centroid, and how far is the centroid from the midpoint?

16 units from vertex to centroid; 8 units from centroid to midpoint.

The centroid divides a median in a 2:1 ratio. One part is 24 ÷ 3 = 8, so the longer segment is 2 × 8 = 16.

Teaching notes

Make the practice count

  • A median joins a vertex to the midpoint of the opposite side.
  • A midpoint divides a side into equal halves.
  • Along a median, the vertex-to-centroid segment is twice the centroid-to-midpoint segment.

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Eight diagrams show all three medians, marked side midpoints and the centroid. Choose integer, decimal or algebraic values.

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Math SheetNameScoreTeacherDateTriangle MediansUse midpoint halves and the centroid's 2:1 ratio to find each missing segment.1. UN = 34. Find UY.QUNYVOCUY =2. JK = 16. Find JQ.DJQKMECJQ =3. UK = 27. Find UC.USYKPQCUC =4. CM = 11. Find PM.PJSMHBCPM =The centroid divides every median in a 2:1 ratio from the vertex.math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateTriangle MediansUse midpoint halves and the centroid's 2:1 ratio to find each missing segment.5. PZ = 12. Find CZ.PBSZYFCCZ =6. RZ = 30. Find RO.TRZOIVCRO =7. JT = 20. Find JA.LJATZQCJA =8. DE = 24. Find DC.DHLEAPCDC =The centroid divides every median in a 2:1 ratio from the vertex.math-sheet.comPage 2 of 2

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