T is the midpoint of MV. If MT = 6x and TV = 3x + 3, find the value of x, MT, TV, and MV.

TV = 3x+9 - (14+2x)

TV = 3x + 9 -14 - 2x

TV =  x - 5  

U = ((3x + 9) + (14 + 2x)) / 2  

U = (5x + 23) / 2

TU = (2(3x + 9) / 2) - (5x+23)/2  

TU = (6x + 18 - 5x -23) /2  

TU = (x - 5) / 2

Since U is the midpt, UV = TU, so UV = (x-5) / 2

TU + UV = TV  

(x-5) / 2 + (x-5) /2 = 2 (x-5) /2 = x-5 = TV

Use a number for x.  Let's use 10.

T is 39, V = 34

U = (39 + 34)/2 = 73/2 = 36.5

TV = 39-34 = 5

TV from our equation is x-5.  10 - 5 = 5.  

TU and UV = (x-5) / 2.   (10-5) /2 = 5/2.

(39-34)/2 = 5/2  

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)

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