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

△ABC∼△GJH

Answer 1

To determine the similarity between the two triangles, we need to compare their angles.

For triangle \( \triangle ABC \):

• \( m\angle A = 47^\circ \)
• \( m\angle B = 36^\circ \)
• Therefore, we can find \( m\angle C \): \[ m\angle C = 180^\circ - (m\angle A + m\angle B) = 180^\circ - (47^\circ + 36^\circ) = 180^\circ - 83^\circ = 97^\circ \]

So, the angles for triangle \( \triangle ABC \) are:

• \( \angle A = 47^\circ \)
• \( \angle B = 36^\circ \)
• \( \angle C = 97^\circ \)

For triangle \( \triangle GHJ \):

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

We need to find \( m\angle H \): \[ m\angle H = 180^\circ - (m\angle G + m\angle J) = 180^\circ - (36^\circ + 97^\circ) = 180^\circ - 133^\circ = 47^\circ \]

So, the angles for triangle \( \triangle GHJ \) are:

• \( \angle G = 36^\circ \)
• \( \angle H = 47^\circ \)
• \( \angle J = 97^\circ \)

Now we can match the angles:

• \( m\angle A = 47^\circ \) corresponds to \( m\angle H = 47^\circ \)
• \( m\angle B = 36^\circ \) corresponds to \( m\angle G = 36^\circ \)
• \( m\angle C = 97^\circ \) corresponds to \( m\angle J = 97^\circ \)

Since all corresponding angles are equal, we conclude that:

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

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