How do we solve similarity problems?

Similar figures are figures that are the same shape, but not necessarily the same size.

If these figures should also be the same size, the figures are called congruent.

Ex) 

Similar triangles wit scale factor of 2

Solving for Similariteis:

1) Solve for X and Y 

       In the triangle ABC shown below, A'C' is parallel to AC. Find the length y of BC' and the length x of A'A

 

Solution: 

• BA is a transversal that intersects the two parallel lines A'C' and AC, hence the corresponding angles BA'C' and BAC are congruent. BC is also a transversal to the two parallel lines A'C' and AC and therefore angles BC'A' and BCA are congruent. These two triangles have two congruent angles are therefore similar and the lengths of their sides are proportional. Let us separate the two triangles as shown below.
  
  
  
  
• We now use the proportionality of the lengths of the side to write equations that help in solving for x and y.
  
  (30 + x) / 30 = 22 / 14 = (y + 15) / y
  
  
• An equation in x may be written as follows.
  
  (30 + x) / 30 = 22 / 14
  
  
• Solve the above for x.
  
  420 + 14 x = 660
  
  x = 17.1 (rounded to one decimal place).
  
  
• An equation in y may be written as follows.
  
  22 / 14 = (y + 15) / y
  
  
• Solve the above for y to obtain.
  
  y = 26.25 

Guided Practice:

 1)Find the length of the missing sides

Citation:
 http://www.analyzemath.com/Geometry/similar_triangle_problems.html
http://www.mathwarehouse.com/geometry/similar/triangles/index.html