Which similarity statement describes the relationship between a triangle with angles m∠A=48°

Question

m
∠
A
=
48
°
, m∠B=17°
m
∠
B
=
17
°
, and m∠C=115°
m
∠
C
=
115
°
and another triangle with angles m∠H=17°
m
∠
H
=
17
°
, m∠I=48°
m
∠
I
=
48
°
, and m∠J=115°
m
∠
J
=
115
°
?(1 point)
Responses

△ABC∼△HIJ
△
A
B
C
∼
△
H
I
J
triangle upper A upper B upper C tilde triangle upper H upper I upper J

△BAC∼△HIJ
△
B
A
C
∼
△
H
I
J
triangle upper B upper A upper C tilde triangle upper H upper I upper J

△BCA∼△JIH
△
B
C
A
∼
△
J
I
H
triangle upper B upper C upper A tilde triangle upper J upper I upper H

△CAB∼△JHI

Answer 1

To determine the correct similarity statement, we need to analyze the corresponding angles in both triangles.

The angles of the first triangle \( ABC \) are:

• \( m\angle A = 48^\circ \)
• \( m\angle B = 17^\circ \)
• \( m\angle C = 115^\circ \)

The angles of the second triangle \( HIJ \) are:

• \( m\angle H = 17^\circ \)
• \( m\angle I = 48^\circ \)
• \( m\angle J = 115^\circ \)

Now, we can match the angles:

• \( m\angle A \) in triangle \( ABC \) corresponds to \( m\angle I \) in triangle \( HIJ \).
• \( m\angle B \) in triangle \( ABC \) corresponds to \( m\angle H \) in triangle \( HIJ \).
• \( m\angle C \) in triangle \( ABC \) corresponds to \( m\angle J \) in triangle \( HIJ \).

Thus, the corresponding angles are:

• \( A \leftrightarrow I \)
• \( B \leftrightarrow H \)
• \( C \leftrightarrow J \)

This means that the triangles \( ABC \) and \( HIJ \) are similar, respecting the order of their corresponding angles as:

• \( \angle A \) corresponds to \( \angle I \)
• \( \angle B \) corresponds to \( \angle H \)
• \( \angle C \) corresponds to \( \angle J \)

Thus, the correct similarity statement is:

\[ \triangle ABC \sim \triangle HIJ \]

So the answer is:

△ABC∼△HIJ