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∼△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∼△HGJ

Answer 1

To determine the similarity between two triangles based on their angles, we first need to find the measures of the missing angles in each triangle.

For triangle \(ABC\):

• Given \(m∠A = 47°\) and \(m∠B = 36°\).
• The sum of angles in a triangle is \(180°\): \[ m∠C = 180° - m∠A - m∠B = 180° - 47° - 36° = 97° \]

So, \(m∠C = 97°\).

For triangle \(GHJ\):

• Given \(m∠G = 36°\) and \(m∠J = 97°\).
• We can find \(m∠H\): \[ m∠H = 180° - m∠G - m∠J = 180° - 36° - 97° = 47° \]

Now we have:

• Triangle \(ABC\) has angles \(47°, 36°, 97°\).
• Triangle \(GHJ\) has angles \(36°, 47°, 97°\).

Since the angles of triangle \(ABC\) are \(47°, 36°, 97°\) and the angles of triangle \(GHJ\) can be rearranged to \(36°, 47°, 97°\), we can state that both triangles contain the same angle measures.

Thus, we have: \[ \triangle ABC \sim \triangle GHJ \]

The correct response is: \[ \triangle ABC \sim \triangle GHJ \]