Question

are these shapes similar? yes no

Explanation:

Step1: Check the ratio of corresponding sides

For the two triangles, we check the ratios of their corresponding sides.
For the first triangle with sides \(30\), \(30\), \(50\) and the second triangle with sides \(24\), \(24\), \(40\).
The ratio of \(30\) to \(24\) is \(\frac{30}{24}=\frac{5}{4}\), and the ratio of \(50\) to \(40\) is \(\frac{50}{40}=\frac{5}{4}\).

Step2: Check the angles

Since the sides are in proportion and the included angles (the angles between the sides) are equal (as the triangles have two sides equal in proportion and the included angles are the ones that are marked as equal in the figure, which is a property of similar triangles when using the Side - Angle - Side (SAS) similarity criterion).

Answer:

yes