Question

Look at triangle PQR. Segment PN is 9 inches.

Which statement is true?

The length of segment PO is 3 inches.

The length of segment PO is 6 inches.

The length of segment RN is 4.5 inches.

The length of segment ON is 4.5 inches.

Answer 1

Ok, those are all medians drawn, intersecting at the centroid, O.

Answer 2

Do you know a theorem about the medians of a triangle?

Answer 3

so it wouldbe this oone The length of segment ON is 4.5 inches.

Answer 4

I can give you a hint: The third choice, "RN=4.5 in." I don't see any information to justify that, so you can eliminate that choice.

Answer 5

Not necessarily. The centroid does not bisect the medians.
In fact, the centroid divides the median into a one-third segment, and a two-thirds segment. You need to find out which segment is the one-third, and which is the two-thirds.
Knowledge of a theorem would help, but when in doubt, draw the thing and measure it.

Answer 6

The length of segment PO is 6 inches.

Answer 7

That seems more reasonable. That picture appears to be drawn nearly to scale and you can see which segments are longer.

Answer 8

so that would be the answer?

Answer 9

Yes, the theorem (i.e. what is always true about this situation) is that the centroid is two-thirds the distance from the vertex to the midpoint of the opposite side.

Answer 10

ok thank u

Answer 11

You can learn more about those by playing around with the Java applets here:
http://illuminations.nctm.org/tools/IGD_lines/MedianProperties.html