Answer :
Purple color figure is similar to the original figure.
Solution:
Property of similar polygon:
Similar polygons have same shape, corresponding angles are congruent and the corresponding sides are in the same ratio.
(1) Compare original figure with green color figure:
Angles of the original figure:
37°, 53° and 90°.
Angles of the green color figure:
67°, 23° and 90°
These two angles of the triangles not congruent angles.
Hence these shapes are not similar.
(2) Compare original figure with yellow color figure:
Angles of the original figure:
37°, 53° and 90°.
Angles of the yellow color figure:
67°, 23° and 90°
These two angles of the triangles are not congruent angles.
Hence these shapes are not similar.
(3) Compare original figure with purple color figure:
Angles of the original figure:
37°, 53° and 90°
Angles of the purple color figure:
37°, 53° and 90°
These two triangles have same shape and congruent angles.
Ratio of the sides:
[tex]$\frac{3}{6}=\frac{1}{2} , \ \frac{4}{8}=\frac{1}{2} , \ \frac{5}{10}=\frac{1}{2}[/tex]
These two triangles have same ratio.
Hence these shapes are similar.
Hence purple color figure is similar to the original figure.