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

Two polygons with the exact same shape space calledsimilar polygons.

You are watching: Similar polygons have congruent sides and congruent angles

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

equivalent angles space equal. The ratios of pairs of corresponding sides must all be equal.

In figure 1, quadrilateralABCD∼ quadrilateralEFGH.


Figure 1 Similar quadrilaterals.

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


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

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


Figure 2 quadrilaterals that are not comparable to one another.

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

In number 3, quadrilateralFGHIis not comparable to quadrilateralJKLM.


Figure 3 Quadrilaterals that are not comparable to one another.

Even though equivalent angles are equal, the ratios of each pair of equivalent 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 similar polygons, and corresponding angle of similar polygons space equal.)

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