All subjects an essential Ideas Parallel lines triangles polygons Perimeter and also Area Similarity appropriate Angles circles Geometric Solids coordinate Geometry

Two polygons with the exact same shape are calledsimilar polygons.

You are watching: If two polygons are similar the corresponding sides are

The symbol because that “is comparable to” is ∼. Notification that it is a part of the “is congruent to” symbol, ≅. As soon as two polygons are similar, these 2 factsbothmust it is in true:

equivalent angles room equal. The ratios of pairs of corresponding sides must all it is in equal.

In figure 1, quadrilateralABCD∼ quadrilateralEFGH.


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Figure 1 Similar quadrilaterals.

This means:mA=mE,mB=mF,mC=mG,mD=mH, and

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It is feasible for a polygon to have one of the over facts true without having the other truth true. The complying with two examples display how the is possible.

In figure 2, square QRST is not similar to square WXYZ.

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Figure 2 square that space not similar to one another.

Even though the ratios of corresponding sides space equal, equivalent angles room not same (90° ≠ 120°, 90° ≠ 60°).

In figure 3, quadrilateralFGHIis not comparable to quadrilateralJKLM.

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Figure 3 Quadrilaterals that space not similar to one another.

Even though corresponding angles are equal, the ratios of each pair of equivalent sides space not same (3/3≠5/3).

Example 1:In number 4, quadrilateralABCD∼ quadrilateralEFGH.(a) FindmE.(b) Findx.

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Figure 4 Similar quadrilaterals.

(a)mE= 90° (∠Eand ∠Aare equivalent angles of comparable polygons, and corresponding angle of similar polygons are equal.)

(b) 9/6 = 12/x(If 2 polygons are similar, then the ratios of each pair of corresponding sides room equal.)