11.5 Similar Triangles Identifying Corresponding Sides of Similar Triangles By: Shaunta Gibson

Similar Triangles are triangles that have the same shape but not necessarily the same size. A B C D E F In the diagram above, triangle ABC is equal to triangle DEF. We write it as ABC ~ DEF. In the diagram, each angle of ABC corresponds to an angle of DEF as follows:

Similar Triangles are triangles that have the same shape but not necessarily the same size. A B C D E F angle A = angle D angle B = angle E angle C = angle F Also, each side of ABC corresponds to a side of DEF AB corresponds to DE BC corresponds to EF AC corresponds to DF

In similar triangles, corresponding sides are the sides opposite the equal angles. * When we write that two angles are similar, we name them so that the order of corresponding angles in both triangles is the same. triangle ABC ~ triangle DEF A B C D E F

Triangle RST ~ triangle XYZ. Name the corresponding sides of these triangles. Because RST ~ XYZ that means angle R = angle X, angle S = angle Y, and angle T = angle Z. Now we write the following: Angle R = Angle X, so ST corresponds to YZ. Angle S = Angle Y, so RT corresponds to XZ. Angle T = Angle Z, so RS corresponds to XY. RS T XY Z

In similar triangles, corresponding sides are in proportion: that is, the ratios of their length are equal. As shown below in the example triangle ABC ~ DEF, therefore we have the following AB BC AC DE EF DF A B C 8 cm 4 cm 6 cm D E F 3 cm 2 cm 4 cm 2 1

Finding the Missing Sides of Similar Triangles To find a missing side of similar triangles To find a missing side of similar triangles 1.) write the ratios of the lengths of the corresponding sides sides 2.) write a proportion using a ratio with known terms 2.) write a proportion using a ratio with known terms and a ratio with an unknown term and a ratio with an unknown term 3.) solve the proportion for the unknown term

In the following diagram, triangle TAP ~ triangle RUN. Find x. Because TAP ~ RUN, we write the ratios of the lengths of the corresponding sides. T A PRU N 15 cm 30 cm x 18 cm 12 cm 9 cm 15 x 9 12 x or

Now cross multiply, then divide to get the length of AP. T A PRU N 15 cm 30 cm x 18 cm 12 cm 9 cm 15 x x = 180: x = 20 so x, or the length of AP, is 20 cm

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