Exercise 40 Page 568

We are given triangle ABC as shown in the following diagram.

It is our goal to draw a triangle that is similar to △ ABC. To do this, we will draw a triangle such that has two pairs of congruent angles with △ ABC. Let's carefully perform the construction step by step.

• Begin by drawing two points, X and Z, and a line that passes through them by using a ruler.
  
• Place the center of a protractor on X so that the line drawn on the bottom portion of the protractor coincides with XZ. Then, locate 34^(∘) on the protractor and mark a point P. This is the measure of ∠ ZXP. Draw a line through X and P to create XP.

• Place the center of the protractor on Z such that its line coincides with XZ. Then, mark a point Q such that the measure of ∠ XZQ is 75^(∘). Draw ZQ.
  
• Let Y be the intersection point between XP and ZQ. By the Angle-Angle (AA) Similarity Postulate, △ ABC ~ △ XYZ.
  

We have drawn a triangle that is similar to △ ABC!