which similarity statements are true? check all that apply. □ △jkl ~ △kml □ △jkm ~ △jkl □ △jkm ~ △kml □ △jmk…

which similarity statements are true? check all that apply. □ △jkl ~ △kml □ △jkm ~ △jkl □ △jkm ~ △kml □ △jmk ~ △jkl □ △jmk ~ △kml

which similarity statements are true? check all that apply. □ △jkl ~ △kml □ △jkm ~ △jkl □ △jkm ~ △kml □ △jmk ~ △jkl □ △jmk ~ △kml

Answer

Brief Explanations:

In right triangle ( \triangle JKL ) (right-angled at ( K )), ( KM \perp JL ). By the right triangle altitude theorem, the altitude to the hypotenuse creates two smaller right triangles similar to the original triangle and to each other. Thus:

  • ( \triangle JKL \sim \triangle JMK \sim \triangle KML ) (all right triangles sharing corresponding angles).
    Check each statement for correct correspondence:
  • ( \triangle JKL \sim \triangle KML ): Correct (original ~ smaller triangle at ( M )).
  • ( \triangle JKM \sim \triangle JKL ): Correct (smaller triangle at ( J ) ~ original).
  • ( \triangle JKM \sim \triangle KML ): Correct (two smaller triangles ~ each other).
  • ( \triangle JMK \sim \triangle JKL ): Correct (same as ( \triangle JKM \sim \triangle JKL ), just vertex order).
  • ( \triangle JMK \sim \triangle KML ): Correct (same as ( \triangle JKM \sim \triangle KML ), vertex order).

Answer:

( \triangle JKL \sim \triangle KML ), ( \triangle JKM \sim \triangle JKL ), ( \triangle JKM \sim \triangle KML ), ( \triangle JMK \sim \triangle JKL ), ( \triangle JMK \sim \triangle KML )