A student writes the following statement: "In and , , ,

MATHEMATICS · Single correct · CBSE · Mathematics · Triangles · Triangles

Problem

A student writes the following statement: "In △ABC\triangle ABC and △DEF\triangle DEF, AB=5 cmAB = 5\text{ cm}, AC=8 cmAC = 8\text{ cm}, DE=7.5 cmDE = 7.5\text{ cm}, DF=12 cmDF = 12\text{ cm} and ∠B=∠E\angle B = \angle E. Since ABDE=ACDF=23\dfrac{AB}{DE} = \dfrac{AC}{DF} = \dfrac{2}{3}, the triangles are similar by the SAS criterion." Which of the following best evaluates the student's statement? (a) The statement is correct; the triangles are similar by SAS. (b) The statement is incorrect; the side ratios are not equal. (c) The statement is incorrect; the equal angle is not included between the proportional sides, so SAS cannot be applied. (d) The statement is incorrect; three equal angles are required to apply SAS.

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