Question

which of these four - sided shapes are similar? select is similar to qrst.

Explanation:

Step1: Recall Similarity Condition

For two polygons to be similar, their corresponding angles must be equal, and their corresponding sides must be in proportion.

Step2: Analyze ABCD

ABCD is a rectangle (all angles \(90^\circ\)) with length \(12\) cm and width \(4\) cm. The ratio of length to width is \(\frac{12}{4} = 3\).

Step3: Analyze QRST

QRST is a rectangle (all angles \(90^\circ\)) with length \(18\) cm and width \(6\) cm. The ratio of length to width is \(\frac{18}{6} = 3\).

Step4: Analyze WXYZ

WXYZ is a parallelogram (angles not necessarily \(90^\circ\)) with sides \(18\) cm and \(6\) cm. But since it's a parallelogram, its angles are not right angles like the rectangles, so corresponding angles won't be equal to QRST's angles.

Step5: Compare Ratios and Angles

ABCD and QRST are both rectangles (so all angles \(90^\circ\), equal corresponding angles) and their side ratios are both \(3\) (proportional sides). WXYZ has different angles (not right angles) so can't be similar to QRST.

Answer:

ABCD (the rectangle with length 12 cm and width 4 cm) is similar to QRST.