Two polygons v the exact same shape space calledsimilar polygons.
You are watching: How to tell if polygons are similar
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:
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 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.
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.
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) Findm∠E.(b) Findx.
See more: How Many Grams In 50 Pounds To Grams, How Many Grams In 50 Lb
Figure 4 Similar quadrilaterals.
(a)m∠E= 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.)