2-8 Proportions and Similar Figures

Objectives

To find missing lengths in similar figures

To use similar figures when measuring indirectly

Image Long Description

In the Solve It, the sailboat and its model have the same shape but they are different sizes. Similar figures have the same shape but not necessarily the same size.

Essential Understanding You can use proportions to find missing side lengths in similar figures. Such figures can help you measure real-world distances indirectly.

The symbol ~ tilde  means “is similar to.” In the diagram, △ A B C ~ △ F G H . white up pointing triangle eh b c tilde white up pointing triangle f g h .

In similar figures, the measures of corresponding angles are equal, and corresponding side lengths are in proportion. The order of the letters when you name similar figures is important because it tells which parts of the figures are corresponding parts. So, because △ A B C ~ △ F G H , white up pointing triangle eh b c tilde white up pointing triangle f g h comma  the following is true.

∠ A ≅ ∠ F ∠ B ≅ ∠ G ∠ C ≅ ∠ H and A B F G = A C F H = B C G H ▲ ▲ ▲ The symbol  ≅  means “is congruent to.” Congruent angles have the same measure. The ratios are equal. table with 3 rows and 1 column , row1 column 1 , angle eh approximately equal to angle f angle b approximately equal to angle g angle c approximately equal to angle h and . fraction eh b , over f g end fraction . equals . fraction eh c , over f h end fraction . equals . fraction b c , over g h end fraction , row2 column 1 , black up pointing triangle black up pointing triangle black up pointing triangle , row3 column 1 , begin box , table with 2 rows and 1 column , row1 column 1 , cap the symbol . approximately equal to . means left double quote markis congruent to.right double quote mark , row2 column 1 , cap congruent angles have the same measure. , end table , end box . begin box , table with 1 row and 1 column , row1 column 1 , cap the ratios are equal. , end table , end box , end table

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