Ms+Gravel's+Class+-+Group+4

=Geometric Proofs...= By Courtney and Marjorie

===Group 4: Create a Trapezoid. Prove that it is a Trapezoid and that a line connecting the midpoints of the non-parallel sides is parallel to the other two sides. ===

a( -4,1) ~ b (4,1)
===The characteristics of a trapezoid, is that is has two parallel lines. It is also a quadrilateral. In order to prove that it is a trapezoid, you have to prove that there are two parallel lines. Find the slope of all four lines and make sure that two are parallel/ have the same slope. ===
 * Part One **


 * To prove it is a trapezoid:**
 * 1. Find the slope of all four sides.**
 * Sab=**
 * __1-1 0__**
 * -4-4 =-8**
 * Sbc=**
 * __5-1 -2__**
 * 2-4 = -1**
 * Scd=**
 * __5-5 0__**
 * -2-2 = -4**
 * Sda=**
 * __5-1 2__**
 * -2--4 = 1**
 * Therefore, ab and cd have the same slope **
 * Therefore, this shape is a trapezoid **


 * Part 2 **
 * Prove that the line connecting the midpoints of the non- parallel sides is parallel to the other sides **
 * Step One: Find the Midpoint of each non parallel side **
 * MP**
 * (__X1+X2, Y1+Y2)__**
 * ___2___ __2__**


 * IN words\/**
 * __(xone plus xtwo over two, yone plus ytwo over two)__**

..........**.(....2.**....**..2..)**
 * MPad=( __-2+-4, 5+1)__**
 * =(-3,3)**


 * MPbc= (__2+4, 5+1)__**
 * .**..........**.(..2.**...**..2.)**
 * = (3,3)**


 * Step 2: Find slope of the line to ensure that it has the same slope as the line ab and cd**

...........**X1-X2** __**3-3 0**__
 * Slope: __Y1-Y2__**
 * 3--3= 6**
 * Therefore, the slope of the line going through the middle of the trapezoid is parallel to the top and bottom line. **