Show the similarity between a triangle with angles A

Question

A
, B
B
, and C
C
, where m∠A=47°
m
∠
A
=
47
°
and m∠B=36°
m
∠
B
=
36
°
, and another triangle with angles G
G
, H
H
, and J
J
, where m∠G=36°
m
∠
G
=
36
°
and m∠J=97°
m
∠
J
=
97
°
.(1 point)
Responses

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

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

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

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

Answer 1

To show the similarity between the triangles \( \triangle ABC \) and \( \triangle GHJ \), we first need to determine the measures of the angles for triangle \( ABC \) and triangle \( GHJ \).

Given:

• For triangle \( ABC \):
  • \( m\angle A = 47^\circ \)
  • \( m\angle B = 36^\circ \)

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

Thus, the angles of triangle \( ABC \) are:

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

Now, for triangle \( GHJ \):

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

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

Thus, the angles of triangle \( GHJ \) are:

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

Now we can compare the angles of both triangles:

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

Since triangles \( ABC \) and \( GHJ \) have the same angles (just in a different order), we can conclude that they are similar.

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