Show the similarity between a triangle with angles A, 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°

Question

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Responses

△ABC∼△GJH

△ABC∼△GJH
- no response given
△ABC∼△HJG
△ABC∼△HJG
- incorrect
△ABC∼△GHJ
△ABC∼△GHJ
- no response given
△ABC∼△HGJ

Answer 1

To determine the similarity between the two triangles, we first need to find the missing angles in both triangles.

For triangle \(ABC\):

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

For triangle \(GHJ\):

• Given: \(m\angle G = 36^\circ\) and \(m\angle J = 97^\circ\).
• Calculate the missing angle \(H\): \[ m\angle H = 180^\circ - m\angle G - m\angle J = 180^\circ - 36^\circ - 97^\circ = 47^\circ. \]

Now we have:

• Triangle \(ABC\) has angles: \(47^\circ, 36^\circ, 97^\circ\).
• Triangle \(GHJ\) has angles: \(36^\circ, 47^\circ, 97^\circ\).

Since both triangles have the same angles, we can conclude:

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

Thus, the appropriate response is:

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