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

△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∼△HJG

Answer 1

To determine the similarity between triangles \( \triangle ABC \) and \( \triangle GHJ \), we first need to find the measure of angle \( C \) using the fact that the sum of the angles in a triangle is \( 180^\circ \).

For triangle \( ABC \):

• \( m\angle A = 47^\circ \)
• \( m\angle B = 36^\circ \)
• Therefore, \( m\angle C = 180^\circ - (47^\circ + 36^\circ) = 180^\circ - 83^\circ = 97^\circ \).

Now, let's list the angles of triangle \( GHJ \):

• \( m\angle G = 36^\circ \)
• \( m\angle J = 97^\circ \)

Since \( m\angle B = 36^\circ \), \( m\angle C = 97^\circ \), and \( m\angle A = 47^\circ \) hasn't been addressed in triangle \( GHJ \) yet, we need to find \( m\angle H \):

• \( m\angle H = 180^\circ - (m\angle G + m\angle J) = 180^\circ - (36^\circ + 97^\circ) = 180^\circ - 133^\circ = 47^\circ \).

Now we can see:

• \( m\angle A = 47^\circ \)

• \( m\angle B = 36^\circ \)

• \( m\angle C = 97^\circ \)

• \( m\angle G = 36^\circ \)

• \( m\angle H = 47^\circ \)

• \( m\angle J = 97^\circ \)

Since both triangles \( \triangle ABC \) and \( \triangle GHJ \) have the same angles, we can conclude:

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

The correct response is:

△ABC∼△GHJ