Question

are these shapes similar?

Explanation:

Step1: Check the ratio of corresponding sides

For triangle \(NPO\) and \(XYW\):
\(\frac{NP}{XY}=\frac{800}{600}=\frac{4}{3}\)
\(\frac{NO}{XW}=\frac{600}{450}=\frac{4}{3}\)
\(\frac{PO}{YW}=\frac{1000}{750}=\frac{4}{3}\)

Step2: Check the angles

Both triangles are right - angled (\(\angle N=\angle W = 90^{\circ}\)) and the other two angles are equal (by AA similarity criterion as the sides are in proportion, the angles will be equal)

Answer:

Yes