State whether the following quadrilaterals are similar or not.
(N/A) Two polygons are similar if:
$1$. Their corresponding angles are equal.
$2$. Their corresponding sides are in the same ratio (proportional).
In quadrilateral $PQRS$ and $ABCD$:
- The sides are in the ratio $PQ/AB = QR/BC = RS/CD = SP/DA = 1.5/3 = 1/2$. Thus,the sides are proportional.
- However,the angles of $PQRS$ are not $90^{\circ}$,while all angles of $ABCD$ are $90^{\circ}$.
Since the corresponding angles are not equal,the quadrilaterals $PQRS$ and $ABCD$ are not similar.
$1$. Their corresponding angles are equal.
$2$. Their corresponding sides are in the same ratio (proportional).
In quadrilateral $PQRS$ and $ABCD$:
- The sides are in the ratio $PQ/AB = QR/BC = RS/CD = SP/DA = 1.5/3 = 1/2$. Thus,the sides are proportional.
- However,the angles of $PQRS$ are not $90^{\circ}$,while all angles of $ABCD$ are $90^{\circ}$.
Since the corresponding angles are not equal,the quadrilaterals $PQRS$ and $ABCD$ are not similar.
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