Question

are these shapes similar?

(image of two rectangles: left rectangle efgh with eh=25 ft, ef=35 ft, right angles at all corners; right rectangle pqrs with rq=20 ft, qp=28 ft, right angles at all corners, and sides rs=28 ft, sp=20 ft)

options: yes, no

Explanation:

Step1: Check the ratio of corresponding sides

For the first shape (rectangle \(EFGH\)) with sides \(25\) ft and \(35\) ft, and the second shape (quadrilateral \(PQRS\)) with sides \(20\) ft and \(28\) ft.
Calculate the ratio of the shorter sides: \(\frac{25}{20}=\frac{5}{4}\)
Calculate the ratio of the longer sides: \(\frac{35}{28}=\frac{5}{4}\)

Step2: Check the angles

Both shapes have four right - angles (as indicated by the right - angle marks).

Since the ratios of the corresponding sides are equal (\(\frac{5}{4}\)) and the corresponding angles are equal (all right - angles), the two shapes are similar.

Answer:

yes