C.  Alternate Investigation

If you are unable to access the Right Triangles applet, complete the following activity.

  1. Draw 4 right triangles and measure the angles in each triangle. Find the sum of the three angles in each triangle. What do you notice?

  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.

One conclusion you may have drawn from the previous investigation is that if two right triangles contain an identical acute angle, the other two corresponding acute angles must also be equal. Both triangles will then have the same three angles and will therefore be similar. In summary, if two right triangles contain an identical acute angle, the two triangles are similar.


So far, you have looked at two important relationships:

  • The ratio of corresponding side lengths of similar right triangles is always the same.

  • Right triangles containing an identical acute angle must be similar.

From these two relationships you can conclude that all triangles containing an identical acute angle have the same ratio of corresponding side lengths.

Use this conclusion to complete the Check Up on the following page.