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∼△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
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 the two triangles, we need to find the measures of the angles in each triangle and see if they correspond.

For triangle ABC:

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

To find \( m\angle C \): \[ m\angle C = 180^\circ - m\angle A - m\angle B = 180^\circ - 47^\circ - 36^\circ = 97^\circ \]

So, the angles in triangle ABC are:

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

For triangle GHJ:

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

To find \( m\angle H \): \[ m\angle H = 180^\circ - m\angle G - m\angle J = 180^\circ - 36^\circ - 97^\circ = 47^\circ \]

The angles in triangle GHJ are:

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

Next, we can see that the angles in triangles ABC and GHJ are:

• Angles correspond as follows:
  • \( m\angle A = 47^\circ \) 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 can conclude that:

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

Thus, the correct response is:

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