wuts the median of a trapezoid?

Question

i have a math problem that is impossible to solve until i know what the median of a trapezoid is so i would really appreciate it if someone would tell me :)

Answer 1

It's the segment that connects the midpoints of the two sides that are not parallel to each other.

Answer 2

I have heard people say "elegant" many time. What exactly does that word mean? The most complicated or the simplest proof? Or maybe just the most beautiful proof? I'll give a proof with my most elegant thoughts. ----- Area is simplest. Here's my reasoning (I have not started the proof just yet, but I assume this should work), the area includes the base and height length. We are "given" the height and the base so the median is the only thing we need to find. b1 = length of base on top b2 = length of base on bottom h = length of height m = length of median h(b1 + b2) / 2 = h(b1 + bm) / 4 + h(b2 + bm) / 4 h(b1 + b2) / 2 = h(b1 + b2 + 2bm) / 4 h(b1 + b2) / 2 = h(b1 + b2) / 4 + h(bm) / 2 h(b1 + b2) / 4 = h(bm) / 2 (b1 + b2) / 2 = bm Q.E.D. ----- EDIT: of the EDIT: *O, the area is actually the height multiplied by the median divided by 2 (which I assume is what you meant). Of course, you can also see this in my proof.* Ignore this! I can't believe I messed this up. But still, my proof does show a relationship with height and median and area. ----- I think I found another way to prove it. Make a rectangle from the trapezoid. How does this help? Look, we have formed two triangles (maybe one) both of which has part of the median. We can use similarity to find the length of the cut off parts and then from knowing the remainder, we find the length of the median. The proof will let you understand what I'm saying. Cut the trapezoid from the bottom base to the shorter upper base. As you can see, we have made two triangles containing a small part of the median. b1 = length of top base b2 = length of bottom base h = height The sum of the base of the triangles are b2 - b1 Note that the cut off part of the median is half of the length of the base for each individual triangle. Therefore, total length of the cut off medians is (b2 - b1) / 2 Remember, we have made a rectangle by cutting the trapezoid. The rectangle has the length the same as the median. The length is also b1. Total length of cut off medians + length of the rectangle = length of the median (b2 - b1) / 2 + b1 = (b1 + b2) / 2 = length of median Q.E.D. ----- OK, I thought of another proof. It's basically the same as the second proof except easier to see. Using one of the slants for the trapezoid, you drag it over so that it reaches the other end of the upper base. We have now created a parallelogram. Other then a parallelogram, a triangle is also made. Using similarity and parallelogram facts, we can find the length of the median. ----- Short and insightful is a very *elegant* definition :-)

Answer 3

It would be the line that indicates the average of the two non-parallel sides. So, for example, if the top and bottom edges are horizontal, the median would be a vertical line through the centre of the trapezoid.

Incidentally, have you ever noticed how "trapezoid" is similar to "trapeze"? Imagine a trapeze drawn in perspective, from the point of view of an acrobat just about to jump on board. There you have it -- the origin of the word.

Answer 4

take the 2 parallel sides of the triangle and average them.

Answer 5

i wish i could help you but i cant :( hahahah