SOLUTION: So I am struggling with some geometry and it is about midsegments. The triangle is named TUV. UV=80,TV=100,and HD=80. The question asks what is TU. The book said the answer is 160.

Question 1064176: So I am struggling with some geometry and it is about midsegments. The triangle is named TUV. UV=80,TV=100,and HD=80. The question asks what is TU. The book said the answer is 160. Can some one please explain how?

Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
You haven't shown a picture of what the triangle looks like. So it's impossible to determine where points H and D are located (in relation to T, U, V).

However, I have a feeling that H and D are midpoints of TV and UV (the order isn't clear). If so, then HD is parallel to TU and HD is half of TU

Since HD is half of TU, we know...
HD = half of TU
HD = (1/2)*TU
80 = (1/2)*TU

Isolate TU by multiplying both sides by 2

80 = (1/2)*TU
2*80 = 2*(1/2)*TU
160 = (2/2)*TU
160 = 1*TU
160 = TU
TU = 160

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The straight line connecting midpoints of two sides of a triangle is parallel to the third side of the triangle.
The mid-segment of a triangle has the measure half of that side.

See the lesson
    - The line segment joining the midpoints of two sides of a triangle
in this site.

Also, you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lessons are the part if this textbook under the topic "Properties of triangles".

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