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

Question

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

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

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

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

△CAB∼△JHI

Answer 1

To determine the similarity statement that describes the relationship between the two triangles based on their angles, we can follow these steps:

We have two triangles:

1. Triangle \( ABC \) with angles:

   • \( m∠A = 48° \)
   • \( m∠B = 17° \)
   • \( m∠C = 115° \)

2. Triangle \( HIJ \) with angles:

   • \( m∠H = 17° \)
   • \( m∠I = 48° \)
   • \( m∠J = 115° \)

To establish similarity, we can compare the angles of both triangles to find corresponding angles:

• \( m∠A \) (48°) corresponds to \( m∠I \) (48°)
• \( m∠B \) (17°) corresponds to \( m∠H \) (17°)
• \( m∠C \) (115°) corresponds to \( m∠J \) (115°)

Since the angles of triangle \( ABC \) can be matched with the angles of triangle \( HIJ \) in the same order, the similarity statement is:

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

Therefore, the correct response is:

△ABC∼△HIJ