Question

write a similarity statement. (\trianglesquaresim\triangle)

Explanation:

Step1: Check the ratio of the sides

We have two sides of one triangle \(35\) and \(56\), and two sides of another triangle \(30\) and \(48\).
The ratio of the first pair of sides: \(\frac{35}{30}=\frac{7}{6}\)
The ratio of the second pair of sides: \(\frac{56}{48}=\frac{7}{6}\)

Step2: Check the included angle

The included angles \(H\) and \(R\) are marked as equal.

Since we have two sides in proportion (\(\frac{35}{30}=\frac{56}{48}=\frac{7}{6}\)) and the included angles equal, by the SAS (Side - Angle - Side) similarity criterion, the triangles are similar.

For the similarity statement, we match the vertices. Let the first triangle be \(\triangle JH\) (assuming the other vertices are named properly, say if the first triangle has vertices \(J\), \(H\) and another and the second has \(T\), \(R\) and another). If we assume the triangles are \(\triangle J H\) (with sides \(35\) and \(56\)) and \(\triangle T R\) (with sides \(30\) and \(48\)), then \(\triangle JH\sim\triangle TR\) (the order of vertices is based on the correspondence of sides and angles. If the full - named triangles are \(\triangle JKH\) and \(\triangle TRS\) (assuming proper vertex naming from the figure, but based on the given information of two sides and the included angle), we can write \(\triangle JKH\sim\triangle TRS\) (the key is that the vertex with the equal angle is in the middle. If we assume the first triangle has vertices \(J\), \(K\), \(H\) and the second \(T\), \(S\), \(R\) with \(\angle K=\angle S\) (the included angle), then \(\triangle JKH\sim\triangle TRS\))

Answer:

The triangles are similar by SAS. The similarity statement is \(\triangle JKH\sim\triangle TRS\) (assuming proper vertex naming based on the figure's structure with the two sides and included angle information)