Question

are these shapes similar?

Explanation:

Step1: Check the side - length ratios

For the first triangle \( \triangle JSH\), sides are \(21\) mm, \(42\) mm, \(42\) mm. For the second triangle \( \triangle MON\), sides are \(21\) mm, \(42\) mm, \(43\) mm.
The ratio of the first pair of sides (both \(21\) mm) is \(\frac{21}{21} = 1\). The ratio of the second pair of sides (both \(42\) mm) is \(\frac{42}{42}=1\). The ratio of the third pair of sides (\(42\) mm and \(43\) mm) is \(\frac{42}{43}
eq1\).

Step2: Use the similarity criterion (SSS - Side - Side - Side)

For two triangles to be similar, the ratios of their corresponding sides must be equal. Since \(\frac{21}{21}=\frac{42}{42}
eq\frac{42}{43}\), the SSS similarity criterion is not satisfied.

Answer:

No, these shapes (triangles) are not similar.