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Show the similarity between a triangle with angles A , B , and C , where m∠A=47° and m∠B=36° , and another triangle with angles G , H , and J , where m∠G=36° and m∠J=97° .(1 point) Responses △ABC∼△HJG triangle upper A upper B upper C similar to triangle upper H upper J upper G △ABC∼△GHJ triangle upper A upper B upper C similar to triangle upper G upper H upper J △ABC∼△HGJ triangle upper A upper B upper C similar to triangle upper H upper G upper J △ABC∼△GJH

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In a triangle, the sum of the angles is always 180°.

For triangle ABC:

  • m∠A = 47°
  • m∠B = 36°
  • Therefore, m∠C = 180° - (m∠A + m∠B) = 180° - (47° + 36°) = 180° - 83° = 97°

For triangle GHJ:

  • m∠G = 36°
  • m∠J = 97°
  • Therefore, m∠H = 180° - (m∠G + m∠J) = 180° - (36° + 97°) = 180° - 133° = 47°

Now we compare the angles of both triangles:

  • Triangle ABC: m∠A = 47°, m∠B = 36°, m∠C = 97°
  • Triangle GHJ: m∠G = 36°, m∠H = 47°, m∠J = 97°

The angles correspond to each other:

  • m∠A = m∠H = 47°
  • m∠B = m∠G = 36°
  • m∠C = m∠J = 97°

Since the angles in triangle ABC are equal to the angles in triangle GHJ, we can establish that the two triangles are similar by the Angle-Angle (AA) similarity criterion.

The correct notation for the similarity of the triangles is: △ABC∼△GHJ

Thus, the correct option is: △ABC∼△GHJ triangle ABC is similar to triangle GHJ.