05+Midsegment+and+Midsegment+Theorem

Midsegments

=By: Dylan Feinstein, Robert Geerlof, and Kyle Van Den Heuvel=

Summary and Explanation: - The mid-segment of a triangle joins the midpoints of two sides of a triangle such that it is parallel to the third side of the triangle.The mid-segment of a triangle joins the midpoints of two sides of a triangle such that its length is half the length of the third side of the triangle. - The midsegment is basically the average of the top and bottom segments. - The formula for finding the midpoint between plotted points is: (x1+x2)/2, (y1+y2)/2

Solving with the mid segment theorem you can find out more sides lengths than just the mid segment. You can find the mid segment by adding the top side and the bottom sides and dividing by two to get your answer. If you are trying to find the mid segment length on a triangle them you take the bottom side and divide it by two and you will have the mid segment length. The same thing goes when you want to find the bottom length and you have the mid segment you double the length.

Rules: -When a mid segment divides a shape the two half's of a side must be equal length. (see example 1) -If a mid segment divides a shape and the two half's do not match up on opposite sides, but they are equal on the same side than it is ok. (see example 2) -When you are trying to find a side length and you have the mid segment length you divide or multiple by two

= __//**HELPFUL LINKS AND SOURCES**//__ = [|Fun and Simple Examples] This link gives simple examples and midsegment problems [|Create Your Own Lengths] This site allows you to customize your triangle and figure out the midsegment yourself! [|Defintions and Problems] This website gives a nice detailed definition of what midsegments are and how to figure them out. [|Must See Video!] This video FULLY explains everything you need to know about midsegments, it goes into full depth. [|In Depth Examples] PurpleMath.com is a credible source that fully explains detailed problems for midsegments. It also explains the midsegment theorem

__**AN EXCELLENT TRAPEZOID PROBLEM**__

THE ANSWER TO THIS PROBLEM IS:

NO= 5 because....

NO= (JM+KL)/2 NO= (6+4)/2 NO=10/2 NO=5

= EXAMPLES = 1.)

If: AD and DB= 6 AE and EC= 7 and BC= 11 WHAT IS DE??

DE= 1/2(BC) 1/2(11) DE= 5.5

2.)



PQ= 1/2(BC) PQ= 1/2(6) PQ=3

3. ** Find the midpoint between (–1, 2) and (3, –6). ** (-1+3)/2, (2-6)/2 2/2, -4/2 (1, -2)