C. Similarity, Angles, and Ratios

C. Similarity, Angles, and Ratios

Knowing that the ratios of corresponding side lengths in similar triangles are always equal is one of the important relationships used in this lesson. Complete the following activity to explore another important relationship.

Investigation

The following applet shows the angles in a right angle triangle. If you are unable to access the applet, skip ahead to the Alternate Investigation on the next page.

Right Triangle

30 January 2014, Created with GeoGebra

1. The applet shows the angles in a right triangle.
   
   

   1. What is the sum of the three angles in the triangle?
      
      

   2. Adjust the triangle and then find the sum of the angles again. Make a prediction about the angle sum of any right triangle.
      
      

2. Use what you learned in part 1 to answer the following questions.
   
   

   1. If two angles in a right triangle are 90° and 50°, what is the measure of the third angle?
      
      

   2. If one acute angle in a right triangle is 25°, what is the measure of the other acute angle?
      
      

3. Is there enough information provided to conclude that the following two triangles are similar? Explain.