Problem 7
This triangle is an equilateral triangle. All sides are the same length (some unknown number which we don't care about). All angles are the same measure each 60 degrees. Set this expression equal to 60 and solve for x
25x - 15 = 60
25x - 15+15 = 60+15 ... add 15 to both sides
25x = 75
25x/25 = 75/25 .... divide both sides by 25
x = 3 which is the answer we want
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Problem 8
For this problem, I've decided to break up the work into separate image files to show how I did the steps. Otherwise, it might be really cluttered to have everything typed here on the same page.
To get the coordinates of point E, check out the image labeled "figure 1". For point G, look at "figure 2".
For proof that EG is parallel to BC, look at "figure 3"
For proof that segment EG is half the length of segment BC, look at "figure 4"
Finally, I've drawn on the diagram to visually show what it all looks like as a summary in "figure 5"