Question

are these shapes similar?
(image of two triangles: triangle dbc with sides db=16 km, bc=20 km, dc=28 km; triangle ihg with sides ih=12 km, hg=15 km, ig=21 km. also has yes and no options.)

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(DBC\) and \(IGH\), we have the following pairs of corresponding sides:

• \(\frac{DB}{IG}=\frac{16}{12}=\frac{4}{3}\)
• \(\frac{BC}{GH}=\frac{20}{15}=\frac{4}{3}\)
• \(\frac{DC}{IH}=\frac{28}{21}=\frac{4}{3}\)

Step2: Check the equality of ratios

Since \(\frac{DB}{IG}=\frac{BC}{GH}=\frac{DC}{IH}=\frac{4}{3}\), by the Side - Side - Side (SSS) similarity criterion, the two triangles are similar.

Answer:

yes