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

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

△ABC∼△HGJ

Answer 1

To determine the similarity between the two triangles based on their angle measurements, we first need to find the missing angles for both triangles.

For triangle ABC:

• Given:

  • m∠A = 47°
  • m∠B = 36°

• To find m∠C: \[ m∠C = 180° - m∠A - m∠B = 180° - 47° - 36° = 97° \]

So, triangle ABC has angles:

• A = 47°
• B = 36°
• C = 97°

For triangle GHJ:

• Given:

  • m∠G = 36°
  • m∠J = 97°

• To find m∠H: \[ m∠H = 180° - m∠G - m∠J = 180° - 36° - 97° = 47° \]

So, triangle GHJ has angles:

• G = 36°
• H = 47°
• J = 97°

Now, we can see both triangles have the same angles:

• Triangle ABC = (47°, 36°, 97°)
• Triangle GHJ = (36°, 47°, 97°)

Since triangles are similar if their corresponding angles are equal, we find that:

• ∠A corresponds to ∠H
• ∠B corresponds to ∠G
• ∠C corresponds to ∠J

Thus, the two triangles are similar.

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