If you know the base angles of a trapezoid, and you know the length of each base, how can you find the length of the median, the line that connects the middle of each base, each base. For example, If one base angle is 33 and the other is 57, one base is 6 an the other is 10, how can I find the length of the line that connects the middle of each base together??
Please give a proof, and if possible, the angle that the line forms
2006-11-10 10:08:16 · 4 answers · asked by kusbetts 2 in Science & Mathematics ➔ Mathematics
Outline: Extend the slanted sides to form a triangle. Then extend the median. It will go through the vertex of the triangle. (you need to think why, but it does) You can find the length of the extended median using trig (base and angle), and then solve for the original length using similar triangles between the small triangle on top and the big triangle.
2006-11-10 10:18:47 · answer #1 · answered by sofarsogood 5 · 0⤊ 0⤋
poorcocoboiboi is correct but I'm not sure if you have the right idea of a median in a trapezoid. You connect the midpoints of the two non-parallel sides; you do not connect the midpoints of the bases.
For your example, the median would be 8
2006-11-10 10:48:12 · answer #2 · answered by MollyMAM 6 · 0⤊ 0⤋
You actually don't have to know the angles.
The median is halfway between the base and cap line, so its length is the average of these lengths: B+C/2.
To prove this, use the midpoint formula.
2006-11-10 10:17:09 · answer #3 · answered by poorcocoboiboi 6 · 0⤊ 0⤋
Please do not answer this question about math by 'vtb'. It is part of an ongoing competition called the USAMTS, which gives you a month to write proofs for five problems. All work has to be your own, and this is a clear violation of that policy. This is not the first time that 'vtb' has used Yahoo answer to solve USAMTS problems. So once again, you are just helping this user cheat on the competition if you answer this question.
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2006-11-11 06:52:25 · answer #4 · answered by Texas Cowgirl 3 · 2⤊ 1⤋