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∼△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

Answer 1

To determine the similarity between the triangles based on their angles, we first need to find the angles of triangle ABC and then compare them to the angles of triangle GHJ.

In triangle ABC:

• \( m∠A = 47° \)
• \( m∠B = 36° \)

We can find \( m∠C \) using the fact that the sum of the angles in a triangle is 180°:

\[ m∠C = 180° - m∠A - m∠B = 180° - 47° - 36° = 97° \]

So the angles of triangle ABC are:

• \( m∠A = 47° \)
• \( m∠B = 36° \)
• \( m∠C = 97° \)

In triangle GHJ:

• \( m∠G = 36° \)
• \( m∠J = 97° \)

To find \( m∠H \):

\[ m∠H = 180° - m∠G - m∠J = 180° - 36° - 97° = 47° \]

So the angles of triangle GHJ are:

• \( m∠G = 36° \)
• \( m∠H = 47° \)
• \( m∠J = 97° \)

Now we can list the angles of both triangles:

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

Since both triangles have the same angle measures, we can conclude they are similar. Therefore:

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

The correct response is:

\(\triangle ABC \sim \triangle GHJ\) (triangle upper A upper B upper C similar to triangle upper G upper H upper J).