Find length of two line segments in parallelogram.

AI Thread Summary
In the discussion about finding the lengths of two line segments in a parallelogram ABCD with a perimeter of 6 and angle <BAD=60, participants explore the geometry of the problem. The challenge arises from the need to establish a system of equations due to the unique properties of the triangle formed by the angle bisectors AM and BM. A key insight is that triangle BMC is equilateral, leading to the relationship BM = BC, which helps in relating the sides of the parallelogram to the triangle. This connection simplifies the problem, allowing for a clearer path to the solution. The discussion emphasizes the importance of recognizing geometric relationships in solving complex problems.
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Homework Statement


ABCD is a parallelogram with <BAD=60. Lines AM and BM bisect Angles BAD and ABC respectively. Perimeter of ABCD is 6. Find lengths of the sides of triangle ABM.

[PLAIN]http://img709.imageshack.us/img709/2440/stumped.jpg



The Attempt at a Solution



I'm stumped. I can't just solve for the lengths of the sides with a simple system, because there's only one value for which that 90 degree triangle will exist. I'm imagining some sort of system of equations to be setup here, but I can't put my finger on what. Can somebody give me a hint as to how best to begin this problem? SO far I've only designated lengths of the inner triangle relative to the length of the hypotenuse (one side of the perimeter of the parallelogram), but these are the special 30 - 60 - 90 length values. Thanks
 
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Notice that BMC is an equilateral triangle so BM = BC. That will give you an equation relating the short side of the parallelogram with the short leg of the right triangle. That should help.
 
Awesome, actually that did help :p. Sometimes it's the simple things that are overlooked.
 

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