Similar Figures Similar Figures Definition of Similar Figures Similar figures are figures that have the same shape but not necessarily the same size. Example: Dr. Evil & Mini-me

Student Expectation: 7 th Grade: 7.3.6D Use critical attributes to define similarity. 8 th Grade: 8.3.6A Generate similar figures using dilations including enlargements and reductions

Similar Figures Two geometric figures are similar if the following condition are true: ● Both figures are the same shape. ● The corresponding angles of the figures are congruent. ● The ratios of the lengths of corresponding sides are equal, so they form a proportion.

Examples of Similar Figures Figures that have the same shape, but do not have the same size, are said to be similar. These two photographs of Sadie are the same shape, but they are not the same size. The photographs are called similar figures.

Examples of Similar Figures The trapezoids shown below are similar; they have the same shape but they are different in size.

Examples of Similar Figures Polygons can still be similar even if one of them is rotated, and/or mirror image of the other. In the figure below, all three polygons are similar

Definition of Similar Figures In mathematics, figures are said to be similar if their corresponding angles are congruent (equal) and their corresponding sides are in proportion.

Finding the Length of an Unknown Side: If you know that two objects are similar, you can use proportions and cross products to find the length of an unknown side. Let's find the length of side DF, labeled x. We can write a proportion, like this: Take the cross product to get the equation: Solve the equation: