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# Geometry (Triangle Theorems)

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Not sure if I'm doing any of these right. Please correct me, thanks.

What is the value of x? (58.6?) What is the value of x? (24?) What is the value of x? (20?) Feb 8, 2018

#1
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The first and third one use the fact that  a line segment drawn parallel to a base splits the sides proportionally

So on the first

MA  =  46.2 - 14  =  32.2

And  we have the following proportion :

MA / MN  =  MB / MP

32.2 /  46.2  =  MB / 72.6       multiply both sides by 72.6

72.6 * 32.2 / 46.2  =  MB   =  x   =  50.6

For the third  one

5x + 10 / 10  =  121 / 11

5x + 10 / 10  =  11    multiply both sides by 10

5x + 10  = 110     subtract 10 from both sides

5x  = 100      divide both sides by 5

x  = 20     CORRECT!!!   Feb 8, 2018
#2
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For...the second.....the  bisected apex   angle   GEH sets up the following proportion :

GD / GE  =  DH / HE

x + 4  / 44.8   =  35 / 56    multiply both sides by 44.8

x + 4  =   44.8 * 35  / 56       simplify

x + 4  =  28      subtract 4 from both sides

x  =  24

Check for youself that  GD / GE  = DH / HE   =  5/8

Hope that helped......!!!!   Feb 8, 2018