Question

are these shapes similar?

Explanation:

Step1: Check the corresponding angles

The first triangle has angles: one right - angle (\(90^{\circ}\)), and two other angles. The second triangle also has angles: one right - angle (\(90^{\circ}\)), and two other angles. Since the sum of angles in a triangle is \(180^{\circ}\), if two angles of one triangle are equal to two angles of another triangle, all three angles are equal.

Step2: Check the ratio of corresponding sides

For the first triangle with sides \(75\) mi, \(100\) mi, \(125\) mi and the second triangle with sides \(75\) mi, \(100\) mi, \(100\) mi.
The ratio of the first pair of corresponding sides (the sides of length \(75\) mi) is \(\frac{75}{75} = 1\).
The ratio of the second pair of corresponding sides (the sides of length \(100\) mi) is \(\frac{100}{100}=1\). But the third side of the first triangle is \(125\) mi and the third side of the second triangle is \(100\) mi, and \(\frac{125}{100}=\frac{5}{4}
eq1\).

Answer:

no