To the middle of the opposite side

The idea

A median of a triangle is the line segment joining a vertex to the midpoint of the opposite side.

Join to the middle

A triangle has 3 vertices. Pick a vertex and join it to the middle of the side facing it. The line segment you get has a name: a median.

How many medians does a triangle have?

• 1
• 3
• 6

Draw the medians

Tap a vertex to draw the median from it. The tick marks show the two equal halves of the opposite side. Do it for both triangles.

Vertex to midpoint

A median of a triangle is the line segment joining a vertex to the midpoint of the opposite side.

The midpoint cuts the opposite side into two equal parts. Each vertex faces one side, so a triangle has three medians, one from each vertex. In triangle ABC, if D is the midpoint of BC, then AD is a median.

Notes

A median of a triangle is the line segment joining a vertex to the midpoint of the opposite side. A triangle has three medians.

Check yourself

Which segment is a median of triangle ABC?

D is the midpoint of side BC, and BC = 14 cm. How long is BD?

Answer: 7 cm

BD = DC = 14 ÷ 2 = 7 cm.

In triangle ABC, the median from B goes to the midpoint of which side?

How many medians does a triangle have in all?

Answer: 3

One median from each of the 3 vertices: 3 medians.

• From A to a point of BC where it meets BC at a right angle. That is the height. It meets BC at a right angle, but not necessarily at the midpoint.
• From A to any point of BC. The point must be the midpoint of BC, the exact middle.
• From A to the midpoint of BC — correct. Yes. A median goes from a vertex to the midpoint of the opposite side.
• AC — correct. Yes. AC is the side opposite B.
• AB. AB touches B. The median goes to the opposite side.
• BC. BC touches B. The median goes to the opposite side.