SOLUTION: Hi - another question we have is "A line passing through the mid-point of one side of a triangle will passt through the mid point of a second side if and only if it is parallel to

Algebra ->  Geometry-proofs -> SOLUTION: Hi - another question we have is "A line passing through the mid-point of one side of a triangle will passt through the mid point of a second side if and only if it is parallel to       Log On


   

Question 215605: Hi - another question we have is "A line passing through the mid-point of one side of a triangle will passt through the mid point of a second side if and only if it is parallel to the third side of the triangle". We think it has to deal with extending lines to make a quadrilateral and then using congruent triangles...but again we are not sure where to go next...
Thanks
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
"A line passing through the mid-point of one side of a triangle will passt through the mid point of a second side if and only if it is parallel to the third side of the triangle". We think it has to deal with extending lines to make a quadrilateral and then using congruent triangles...but again we are not sure where to go next...
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Draw the figure.
Notice the two overlapping triangles.
Notice that two of the sides are transversals cutting the two
parallel sides (the base of the larger and the base of the smaller triangle)
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Using AAA you can show the two triangles are similar.
You can then conclude what you are trying to prove.
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Cheers,
Stan H.