Explore the Lesson

B. Side Ratios in Similar Triangles

Investigation

The following applet explores a relationship that is true for all similar triangles. If you are unable to access the applet, skip ahead to the Alternate Investigation on the next page.

Similar Right Triangles

29 January 2014, Created with GeoGebra

The two triangles shown in the applet are similar and both include a right angle. They can be adjusted by changing the scale factor and by moving the points and . Use the applet to answer the following questions.

  1. Knowing that is similar to , what relationship do you expect between angles and , and and ? Turn on "Show Angles" to confirm your prediction.

  2. Turn off "Show Angles" and turn on "Show Ratios" so the ratios and are shown.

    1. Explain how and are calculated.

    2. Keep an eye on the ratios as you change the triangles by moving points and . What do you notice about the relationship between the values of and ?

    3. Try to explain the relationship you noticed in part b.

  3. Suppose .

    1. What does this tell you about the size of compared to the size of ?

    2. If , while , what must be the length of ? Try to answer without using the applet.