Geometry
# Similar Polygons

Are the rectangles with dimensions

$2 \times 5 \text{ and } 12 \times 9$

similar?

Quadrilaterals $ABCD$ and $EFGH$ satisfy $AB = 2EF, BC = 2FG, CD =2GH, DA = 2HE$.

Must they be similar?

Are the rectangles with dimensions

$8 \times 5 \text{ and } 25 \times 40$

similar?

Are the parallelograms with side lengths

$4 \times 15 \text{ and } 60 \times 16$

similar?

Consider parallelograms $ABCD$ and $EFGH$. We know that $AB = 2, BC = 9, EF = 4, FG = 18$, $\angle ABC = 40^\circ$ and $\angle EFG = 140^ \circ$.

Are these parallelograms similar?