7-2 Similar Polygons

Similar polygons are polygons that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

The similarity statement for triangles indicates that two triangles are similar. It is written using the symbol '∼'. For example, if triangle ABC is similar to triangle DEF, it is written as ΔABC ∼ ΔDEF.

Two triangles are similar if: 1) Their corresponding angles are equal (Angle-Angle or AA criterion), or 2) The lengths of their corresponding sides are proportional (Side-Side-Side or SSS criterion), or 3) Two sides are proportional and the included angle is equal (Side-Angle-Side or SAS criterion).

The value of x in similar polygons often represents a length or measurement that can be found using the properties of similar figures, such as proportionality of corresponding sides.

The ratio of similarity is the ratio of the lengths of corresponding sides of two similar polygons. It is constant for all pairs of corresponding sides.

Two figures are similar if they have the same shape, which means their corresponding angles are equal and their corresponding sides are in proportion.

To solve for a missing side length in similar polygons, set up a proportion using the lengths of corresponding sides and solve for the unknown variable.

The Angle-Angle (AA) criterion states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

The Side-Side-Side (SSS) criterion states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

The Side-Angle-Side (SAS) criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.