Right triangle, hypotenuse 13, find the median to it

Step by step

The question

Question: in a right triangle the hypotenuse B C is 13: find the median A M to the hypotenuse.

1 Use the semicircle rule

The right angle is at A.

The median A M goes to M, the middle of the hypotenuse B C.

Draw the circle with B C as its diameter.

The angle in a semicircle is 90°, so A is on this circle too.

M is the center.

M A, M B and M C are all radii: all the same length.

2 Half the hypotenuse

The radius is half the diameter: 13 divided by 2 is 6.5.

Careful!

This works for the median to the hypotenuse of a right triangle.

Not for any median.

3 Check

Let's check: M B and M C are 6.5 each, and together they make B C, 13.

So it is right!

Let's look back.

First: use the semicircle rule.

Then: half the hypotenuse.

Last: check.