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sqdancefan

Answer:

  • ABC -- not similar
  • ΔJKL ~ ΔHIG, AA similarity
  • not similar

Step-by-step explanation:

a) Side ratios in the smaller triangle are 3:4:6. In the larger triangle, they are 5:6:9. These are not equivalent ratios, so the triangles are not similar.

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b) The missing angle in the left triangle is 90° -55° = 35°. This matches the acute angle shown in the right triangle, so the right triangles are similar by the AA similarity criterion. The given triangle JKL starts with the largest acute angle, then the right angle, so the similarity statement must be ...

  ΔJKL ~ ΔHIG

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c) All we know for sure is that the vertical angles are congruent. We need information about a pair of sides or of another angle before any similarity can be claimed. The triangles are not necessarily similar.

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