Similar Triangles

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Similar figures are geometrical figures that have the same shape but are not necessarily of the same size. All corresponding angles are equal and all corresponding sides are in proportion. Examples:

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Two polygons with the same number of sides are similar if: 1. All corresponding angles are equal AND 2. All corresponding sides are in the same ratio (proportion) Both conditions must be satisfied f

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The scale factor is the ratio of corresponding sides of similar figures. If scale factor k = corresponding side of figure 1/corresponding side of figure 2, then: • If k > 1: Figure 1 is enlarged com

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**Basic Proportionality Theorem (Thales Theorem):** If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in

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**Converse of Basic Proportionality Theorem:** If a line divides two sides of a triangle in the same ratio, then the line is parallel to the third side. In △ABC, if AD/DB = AE/EC, then DE || BC Thi

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**AAA Criterion for Similarity:** If in two triangles, corresponding angles are equal, then their corresponding sides are in proportion and the triangles are similar. **AA Criterion:** If two angles

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**SSS Criterion for Similarity:** If in two triangles, corresponding sides are proportional, then their corresponding angles are equal and the triangles are similar. In △ABC and △DEF: If AB/DE = BC/

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**SAS Criterion for Similarity:** If one angle of a triangle is equal to one angle of another triangle and the including sides of these angles are proportional, then the two triangles are similar. I