Lesson 11.4 • Corresponding Parts of Similar Triangles

Lesson 11.4 • Corresponding Parts of Similar Triangles (continued)Step 7To finish constructing triangle ABC, hide all partsof triangle ABC except point A and construct themissing segments of the new triangle. Change yourratio and observe the results.BBIn Steps 8–10, you’ll construct altitudes in the similartriangles and measure their ratio.AmnACm__n 0.7CStep 8Select a vertex of one triangle and the side oppositethat vertex, and choose Construct ⏐ Perpendicular Line.Construct the point where the perpendicular intersectsthe side, construct the segment, and hide the line.Step 7Step 9Step 10Do the same in the other triangle.To measure the ratio between the altitudes,select the shorter altitude, then the longeraltitude, and choose Measure ⏐ Ratio.ABBC ACorresponding AltitudesCInvestigate1. Drag parts of your sketch and observe the ratio of the altitudes. Recordyour observations.SketchIn Steps 11 and 12, you’ll construct medians in your triangles and measuretheir ratio.Step 11Step 12Delete or hide the altitudes, and construct a pair of correspondingmedians.Measure the ratio of the medians. (For consistency, select themedian on ABC first.)BBACACCorresponding MediansInvestigate2. Drag parts of your sketch and observe the ratio of the medians. Recordyour observations.(continued)142 CHAPTER 11 Discovering Geometry with The Geometer’s Sketchpad©2008 Key Curriculum Press