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

△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∼△GJH

Answer 1

To determine the similarity between triangle \( \triangle ABC \) and triangle \( \triangle GHJ \), we first need to find the measures of all angles involved.

For triangle \( \triangle ABC \):

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

So, triangle \( \triangle ABC \) has angles \( 47° \), \( 36° \), and \( 97° \).

For triangle \( \triangle GHJ \):

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

So, triangle \( \triangle GHJ \) has angles \( 36° \), \( 47° \), and \( 97° \).

Now we can compare the angles of the two triangles:

• \( \triangle ABC \): \( 47° \), \( 36° \), \( 97° \)
• \( \triangle GHJ \): \( 36° \), \( 47° \), \( 97° \)

Since both triangles have the same angle measures, we can conclude that:

\[ \triangle ABC \sim \triangle GHJ \]

Therefore, the correct response is: \[ \triangle ABC \sim \triangle GHJ \]