All subjects basic Ideas Parallel present triangle polygon Perimeter and also Area Similarity best Angles one Geometric Solids coordinate Geometry

Two polygons v the exact same shape space calledsimilar polygons.

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

matching angles are equal. The ratios of pairs of corresponding sides need to all be 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 the the above facts true without having actually the other reality true. The adhering to two examples show how that is possible.

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

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Figure 2 quadrilaterals that room not similar to one another.

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

In figure 3, quadrilateralFGHIis not similar to quadrilateralJKLM.

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Figure 3 Quadrilaterals that are not comparable to one another.

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

Example 1:In figure 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 angles of comparable polygons room equal.)

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