Take a look at [math]\Delta[/math][color=#0000ff]ABC[/color] and [math]\Delta[/math][color=#6aa84f]DEF[/color] and compare them. What do they have in common? What is different about them?[br][br]You may have noticed that they have equivalent angles. [math]\angle a=\angle d[/math], [math]\angle b=\angle e[/math], and [math]\angle c=\angle f[/math]. Now, the side lengths are not the same, but what if we take a look at the ratios between the side lengths. Take a moment to calculate [math]\frac{AB}{DE}[/math], [math]\frac{AC}{DF}[/math], [math]\frac{BC}{EF}[/math] and round your answer to two decimal places. What do you notice?[br][br]You may have noticed that they are all equal! This is true for all triangles that share equivalent interior angles. Move points B and E around to get new dimensions and calculate the above ratios again. Did you get the same thing?[br][br]Are you able to make it so that each triangle has the same side lengths?

When two triangles have the same interior angles, we say that they are [b][u]similar triangles[/u].[/b][br][br]Properties of Similar Triangles[br][list][*]Interior angles of both triangles are the same[/*][*]The ratios of their corresponding sides are equal.[/*][/list][br]If two similar triangles also have equivalent side lengths. then we say they are [b][u]congruent triangles.[/u][/b]