geometry (please explain)

Question

Decide whether the triangles are similar. If so, determine the appropriate expression to solve for x.

 The triangles are not similar; no expression for x can be found.

 ΔABC ~ ΔDEF;  

ΔABC ~ ΔEFD; 

 ΔABC ~ ΔFDE; 

Answer 1

Using the property that the sum of the three angles of a triangle is 180 degrees, we can see that angle B is 65 degrees and angle E is 62 degrees. Thus, with all three angles of the two triangles matching the triangles are similar by the angles (AA) test.

Also corresponding sides of similar triangles are in the same proportion. In this case x and z are sides opposite to the 53 degree angle while w and r are sides opposite to the 62 degree angle. That means x/z = w/r. You can work out x accordingly.