7. find the value of x in the triangle. show work to receive credit. (2 points) (picture included) 8. find midsegment (eg) ̅ that is parallel to side (bc) ̅. show all work to receive credit. (3 points) (picture included)

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"

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions