IM 8.2.9 Lesson: Side Length Quotients in Similar Triangles

Triangle  has side lengths 2, 3, and 4. Triangle  has side lengths 4, 5, and 6. Is Triangle  similar to Triangle ?

Triangle  is similar to triangles , , and . The scale factors for the dilations that show triangle  is similar to each triangle are in the table. Find the side lengths of triangles , , and . Record them in the table.

Your teacher will assign you one of the three columns. For all four triangles, find the quotient of the triangle side lengths assigned to you and record it in the table. What do you notice about the quotients?

Compare your results with your partners’ and complete your table.

Explain why .