Show the similarity between a triangle with angles A

Question

, 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∼△GJH
triangle upper A upper B upper C similar to triangle upper G upper J upper H

△ABC∼△HGJ
triangle upper A upper B upper C similar to triangle upper H upper G upper J

△ABC∼△GHJ
triangle upper A upper B upper C similar to triangle upper G upper H upper J

△ABC∼△HJG

Answer 1

To determine the similarity between the two triangles, we first need to find the remaining angles of each triangle.

For triangle ABC:

• Given:
  • m∠A = 47°
  • m∠B = 36°

To find m∠C:

• m∠C = 180° - m∠A - m∠B
• m∠C = 180° - 47° - 36° = 97°

So, the angles of triangle ABC are:

• A = 47°
• B = 36°
• C = 97°

For triangle GHJ:

• Given:
  • m∠G = 36°
  • m∠J = 97°

To find m∠H:

• m∠H = 180° - m∠G - m∠J
• m∠H = 180° - 36° - 97° = 47°

So, the angles of triangle GHJ are:

• G = 36°
• H = 47°
• J = 97°

Now we can pair the angles of the triangles:

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

Since all three pairs of corresponding angles are equal, we can conclude that the triangles are similar.

Thus, we can express the similarity as follows:

• △ABC ∼ △GHJ

So the correct response is: △ABC ∼ △GHJ (triangle A B C similar to triangle G H J)