PEAZIT Aha card
Go straight to resources ↓Triangle medians: vertex to the opposite midpoint
A median joins a vertex to the opposite side’s midpoint. The three medians meet at the centroid; the part from the vertex is twice the remaining part.
| Point or segment | Property |
|---|---|
| S on BC | BS = SC |
| AS = 12 cm | AT = 8 cm, TS = 4 cm |
| AT : TS | 2 : 1 |
One worked example
- BS = SCFind midpoint S of BC first, then connect A to S.
- 12 ÷ 3 = 4 cmSplit the whole median into three equal lengths.
- AT = 2 × 4 = 8 cmTwo parts run from the vertex to the centroid; one continues to the midpoint.
Watch out: A median is not generally an altitude: it need not meet the side at a right angle. It lies inside every nondegenerate triangle.
Goal, prerequisites and card origin
What you will learn: Draw a median and use the centroid to divide its length.
What you need first: Triangle vertices, segment midpoints and thirds.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Khan Academy: triangle medians and centroids ↗Show connections
A median joins a vertex to the opposite side’s midpoint. The three medians meet at the centroid; the part from the vertex is twice the remaining part.