Similar FiguresSimilar FiguresDefinition 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:7th Grade:7.3.6D Use critical attributes to define

similarity.

8th Grade:8.3.6A Generate similar figures using

dilations including enlargements and reductions

Similar FiguresTwo 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 FiguresThe trapezoids shown below are similar; they

have the same shape but they are different in size.

Examples of Similar FiguresPolygons 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 FiguresIn 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: