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Triangle HIJ is similar to triangle DFG.  Find the value of x, y, and z.

 

 Mar 3, 2021
 #1
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The angle will still be the same, no matter what size, so z is still 34 degrees.

Notice that 9 and 5 are the only measurements that stay. 

To find the proportion (idk if thats the right word) between the two triangles, we make a fraction, \(\frac{5}{9}\). We do this so that we can figure out the lengths of each side by multiplying and/or dividing.

 

To find y, we multiply 18 by \(\frac{5}{9}\), getting 10, so y is 10.

 

To find x, we have to DIVIDE 8 by \(\frac{5}{9}\), since unlike y, x is on the left triangle.

8 divided by \(\frac{5}{9}\)is 14.4, so x is 14.4.

 

So the final answer is:

x = 14.4

y = 10

z = 34 degrees

 

Correct me if I'm wrong! smiley

 Mar 3, 2021
edited by swag123456  Mar 3, 2021

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