Math and Arithmetic
Algebra
Geometry

# How can you tell whether two polygons are similar?

###### Wiki User

Polygons will be similar if they have the same number of sides AND all of their angles are the same. All of their angles are the same if all but one of their angles are the same because with the same number of sides the angles must add up to the same thing.

All squares are similar (4 right angles and sides of equal lenght).

All rectangles are similar (4 right angles).

We know two triangle are similar if two or mare angles are the same, or if one angle is the same and the two adjacent sides are the same length. Variations of this last proof may apply to some other polygons.

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## Related Questions

Two polygons are similar if and only if the corresponding angles are congruent

Any two polygons with a different number of sides are not similar.

Yes, the corresponding sides of two similar regular polygons must have equal lengths. This is because both the polygons are similar, which means that since they are also polygons, they must have equal lengths.

similar polygons may not be congruent (different sizes) congruent polygons are always similar (equal in every geometric respect - including

Yes, regular polygons will have all sides equal length, and all angles the same. If two polygons of the same number of sides are 'regular' then those two polygons will be similar (they may be scaled, for example).

Similar polygons are polygons for which all corresponding angles are congruent and all corresponding sides are proportional. From this definition we can say they have the same shape.

Yes. The polygons must be congruent. They must have an even number of sides and angles. -alessandra

If two polygons are similar then the ratio of their perimeter is equal to the ratios of their corresponding sides lenghts?

no, they could be different size but same shape and be similar but not congruent.

Two polygons are similar if:the ratio of the lengths of their corresponding sides is the same, andtheir corresponding angles are equal.

If all angles of two polygons are the same the figures are similar (irrespective of rotation).

The angles are the same, but the sides don't have to be the same length. or Two polygons are similar if and only ifthe corresponding angles are congruentThe corresponding sides must be in a consistent ratio -- for example, if side AB = (2xA'B'), then sides B'C', C'D' ... K'A' must also be twice as long as their corresponding sides BC, CD, ... KA.

Their sides are proportional and their interior angles are the same

The question cannot be answered without information about the relative sizes of the two polygons.

Two geometric shapes are similar if they differ only in their size. For polygons this requires that the corresponding angles of the two polygons are congruent and that the ratio of their corresponding sides is the same.

No. You can have two triangles that are congruent to one another, and two quadrilaterals that are congruent to one another. But the triangle cannot be similar to the quadrilateral!