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°
.(1 point)
Responses

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

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

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

△ABC∼△GJH

1 answer

To determine the similarity between the two triangles, we first need to calculate the missing angles.

In triangle \(ABC\):

  • Given \(m\angle A = 47^\circ\) and \(m\angle B = 36^\circ\).
  • We can find \(m\angle C\) using the triangle sum theorem (the sum of the angles in a triangle is \(180^\circ\)):

\[ m\angle C = 180^\circ - m\angle A - m\angle B = 180^\circ - 47^\circ - 36^\circ = 97^\circ \]

Now we have the angles for triangle \(ABC\):

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

In triangle \(GHJ\):

  • Given \(m\angle G = 36^\circ\) and \(m\angle J = 97^\circ\).
  • We can find \(m\angle H\) using the same theorem:

\[ m\angle H = 180^\circ - m\angle G - m\angle J = 180^\circ - 36^\circ - 97^\circ = 47^\circ \]

Now we have the angles for triangle \(GHJ\):

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

Now we can compare:

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

Since all corresponding angles of triangle \(ABC\) and triangle \(GHJ\) are equal, we have:

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

Thus, the correct response is:

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