Question

are these shapes similar? no yes

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(ABC\) and \(MNO\), we have:

• \(\frac{AB}{NO}=\frac{900}{600}=\frac{3}{2}\)
• \(\frac{BC}{OM}=\frac{675}{450}=\frac{3}{2}\)
• \(\frac{AC}{MN}=\frac{1125}{750}=\frac{3}{2}\)

Step2: Check the AA (Angle - Angle) similarity criterion

Both triangles are right - angled (\(\angle B = \angle O=90^{\circ}\)) and we have already shown that the ratios of their corresponding sides are equal. By the AA similarity criterion (if two angles of one triangle are equal to two angles of another triangle and the sides including these angles are in proportion, the triangles are similar), since the right angles are equal and the sides adjacent to the right angles are in proportion (\(\frac{AB}{NO}=\frac{BC}{OM}\)), and the hypotenuses are also in proportion (\(\frac{AC}{MN}\)), the triangles are similar.

Answer:

yes