Condition For Similarity

Geometry Level 4

Statement: Polygons A1A2A3An A_1 A_2 A_3 \ldots A_n and B1B2B3Bn B_1 B_2 B_3 \ldots B_n are similar polygons.

Condition: The ratio of the corresponding sides of the polygons is constant, i.e.

A1A2B1B2=A2A3B2B3==An1AnBn1Bn=AnA1BnB1\frac{A_1A_2}{B_1B_2} = \frac{A_2A_3}{ B_2B_3} = \cdots = \frac{A_{n-1} A_n}{B_{n-1} B_n} = \frac{A_nA_1}{ B_nB_1}

For the statement to be true, the given condition is ___________.


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