Course Guide - USAID Teacher Education Project

Make sure students realize that a similar shape’s corresponding angles are the sameeven though its corresponding sides differ in length. The next activity will focus onhow the proportionality of side lengths is a key "factor" in similarity.d) On a sheet of graph paper have students draw three rectangles:o 1 units x 2 unitso 5 units x 6 unitso 4 units x 8 unitsDo they think these three rectangles "look similar”? (Each has four 90° angles so theangle principle of similarity holds true.)What do students notice as they compare the side lengths of these rectangles? Dostudents notice differences in proportion that occurred when adding 4 to bothdimensions of the original 1 x 2 rectangle? Can addition of equal units tocorresponding sides justify similarity (1 + 4 = 5, and 2 + 4 = 6)?What happened when the original 1 x 2 rectangle had each of its side lengthsmultiplied by 4 resulting in the 4 x 8 rectangle? Are rectangles 1 and 3 similar? If so,why? If not, why not?e) Summary: Summarize this section of today's lesson on similarity by asking thefollowing questions:• How does the side length property relate to the term "scale factor"?• How can knowing the scale factor help solve for missing sides on twosimilar figures?• In the rectangle problem, there were still four 90° angles, yet all thefigures were not similar. What is the role of angles in similarity?• What does the word "corresponding" imply? Can one double the sidelength and double the angle measurement and still have two similarfigures?• How do the two components of similarity (corresponding angles andcorresponding side lengths) provide a working definition of similarity?f) Have students sketch three 90° angles on grid paper. These will become theirreference angles. How might they:• Find 45°, 22.5°, and 135° angles by using one of the 90° angles that theydrew?• Use another of their 90° angles to estimate angles of 60°, 30°, and 120°?• Use their third 90° angle to find a 180° (straight) angle and a 360° (fullrotation) angle?Once students have done this, ask them to describe the usefulness of a 90° angle as areference or "benchmark" angle to help estimate and compare angles.