7.3 Exploring Similar Right Triangles
Expectations
- determine, through investigation, the relationship between the ratio of two sides in a right triangle and the ratio or the two corresponding sides in a similar right triangle, and define the dine, cosine, and tangent ratios.
A. Construct a diagram like the one shown in your text on page 391. Make sure that angle A equals 40 degrees. Also make sure that all the vertical lines are perpendicular to AB.
B. Explain why the four right triangles in your diagram are similar.
C. For each triangle in your diagram, measure the lengths of the opposite side and the adjacent side, as well as the hypotenuse. Record these values in a table like the one on the top of page 392 in your text. Calculate each ratio to two decimal places.
C. For each triangle in your diagram, measure the lengths of the opposite side and the adjacent side, as well as the hypotenuse. Record these values in a table like the one on the top of page 392 in your text. Calculate each ratio to two decimal places. Use the spreadsheet view to construct your table.
D. Describe the relationship in your table.
E. Do you think the relationships you described in part D would change if angle A changed to a different measure? Make a conjecture (record it here), and then test your conjecture by creating a new diagram using a different acute angle for angle A. Use the measure of this angle to repeat part C.
Test your conjecture from Part E.
Record your new results.