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:
In figure 1, quadrilateralABCD∼ quadrilateralEFGH.
Figure 1 Similar quadrilaterals.
This means:m∠A=m∠E,m∠B=m∠F,m∠C=m∠G,m∠D=m∠H, 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) Findm∠E.(b) Findx.
See more: Driving Distance From Seattle To Boise Idaho, It'S Better To Fly From Seattle To Boise
Figure 4 Similar quadrilaterals.
(a)m∠E= 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.)