Question

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write a similarity statement relating the three triangles in the diagram.
choose the correct answer below.
△jkl - △jlm - △lkm
△jkl - △jml - △lmk
△jlk - △jlm - △lmk

Explanation:

Step1: Recall similarity criteria for right - angled triangles

For right - angled triangles, if the corresponding angles are equal (by AA - Angle - Angle similarity criterion, since all right angles are equal and one common acute angle), the triangles are similar.
In the given figure, \(\triangle JKL\), \(\triangle JLM\), and \(\triangle LKM\) are right - angled triangles.
\(\triangle JKL\) and \(\triangle JLM\) have \(\angle J\) common and both have a right - angle (\(\angle JML\) and \(\angle JLK\)).
\(\triangle JKL\) and \(\triangle LKM\) have \(\angle K\) common and both have a right - angle (\(\angle KML\) and \(\angle KLJ\)).
\(\triangle JLM\) and \(\triangle LKM\) are also similar by AA criterion.

Answer:

\(\triangle JKL\sim\triangle JLM\sim\triangle LKM\)