Question

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Explanation:

Step1: Check corresponding angles and sides

In \(\triangle ABC\) and \(\triangle DEF\), \(\angle A = 35^{\circ}\), \(\angle B=100^{\circ}\), \(\angle C = 45^{\circ}\); \(\angle D = 100^{\circ}\), \(\angle E=35^{\circ}\), \(\angle F = 45^{\circ}\). Also, \(AB = 10\mathrm{cm}\), \(BC = 8\mathrm{cm}\), \(AC = 14\mathrm{cm}\); \(DE = 20\mathrm{cm}\), \(EF = 16\mathrm{cm}\), \(DF = 28\mathrm{cm}\).
We can see that \(\frac{AB}{DE}=\frac{10}{20}=\frac{1}{2}\), \(\frac{BC}{EF}=\frac{8}{16}=\frac{1}{2}\), \(\frac{AC}{DF}=\frac{14}{28}=\frac{1}{2}\), and \(\angle A=\angle E\), \(\angle B=\angle D\), \(\angle C=\angle F\)

Step2: Apply the similarity criterion

By the Side - Angle - Side (SAS) similarity criterion (if the ratios of the corresponding sides of two triangles are equal and the included angles are equal, the triangles are similar) or Side - Side - Side (SSS) similarity criterion (if the ratios of the corresponding sides of two triangles are equal, the triangles are similar). Here, since \(\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}\) and \(\angle A=\angle E\), \(\angle B=\angle D\), \(\angle C=\angle F\), \(\triangle ABC\sim\triangle EDF\)

Answer:

\(\triangle ABC\cong\triangle EDF\)