Consider a triangle and draw one median. Consider an isosceles triangle whose base is half the length of the side corresponding to the median and whose height is half the length of the median.
See solution.
Practice makes perfect
Let's begin by drawing a triangle and one of its medians.
To draw the second required triangle, we start by drawing a segment of length 6/2=3 and mark its midpoint.
Then we draw a point R such that SR= 3.4/2=1.7.
Next, we draw PR and QR and that way we get △ PQR. Also, let's find the measures of its sides and one median.
Now, lets find CD RS and AB PQ.
CD/RS = 3.4/1.7 = 2 =
6/3 = AB/PQ
As we can see, the measures of corresponding medians and a corresponding side are proportional. However, notice that the remaining two corresponding sides of the triangles are not proportional. That is, the triangles are not similar.
△ ABC ≁ △ PQR
Keep in mind that the triangles drawn above are just an example and your answer may vary.
