Similar Figures and Proportions
The Case of Triangles
In order to determine if two triangles are similar we must compare the ratios of each corresponding side. The ratios are written by placing the lengths of each line segment in triangle one over its counterpart in triangle two. Each ratio is separated by a "questioned equal" sign. This equal sign below a question mark represents the uncertainty of the ratio's equality. Once equality or inequality is established the appropriate sign can replace the "questioned equal".
If the ratios of the triangle's corresponding line segments are proportional, then the corresponding angles must have equal values.
The Case of Quadrilaterals and Other Polygons
In figures with four or more sides, it is possible for the corresponding side lengths to be proportional and the figures to have different shapes. To determine if these figures are similar, first check that their corresponding angles have equal measures.
Determining Whether Two Four-Sided Figures are Similar
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