Similar shapes are shapes that have the same general shape but are different sizes. Use the applet below to explore the properties of similar shapes.

[br][br][b]a. What relationships exist between the angle[br]measurements of similar shapes? Will similar shapes always follow this pattern?[br][/b][br][br][br]The corresponding angles of similar shapes are always equal.[br]Yes, similar shapes always follow this pattern.[br][br][br] [br][b]b. What relationships exist between the side length[br]measurements of similar shapes? [/b][br][br][br]The ratios of corresponding side lengths in similar shapes[br]remain constant.[br][br][br][br][b]c. How can you use the scale factor between the shapes to[br]find an unknown length? [/b][br][br][br]Multiply the known side length by the scale factor to find[br]an unknown length. Since the scale factor between triangles ABC and DEF is [b]2[/b],[br]you can find an unknown length by multiplying a corresponding side from the[br]smaller triangle by [b]2[/b].[br][br][br][br][br][b]d. How can you use the side length measurements of[br]similar shapes to calculate the scale factor?[/b][br][br][br]Divide the length of one side of a shape by the[br]corresponding side length of the similar shape to find the scale factor. Divide[br]the length of a side in the larger triangle by the corresponding side in the[br]smaller triangle. Triangle DEF has a side of [b]5 units[/b] and the[br]corresponding side in Triangle ABC is [b]2.5 units[/b], then: 5/2.5=2 This[br]means Triangle DEF is [b]twice the size[/b] of Triangle ABC.[br][b] [/b][br][br][br][b]e. Consider the ratio of two side lengths of a triangle,[br]such as CB/AC. What is the value of this ratio? How does this ratio compare to[br]the ratio of corresponding side lengths on a similar shape, such as FE/DF?[/b][br][br][br]The ratio CB/AC is equal to the ratio FE/DF, as[br]corresponding side ratios in similar shapes are always the same.[br][br][br]