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

△CAB∼△JHI
triangle upper C upper A upper B tilde triangle upper J upper H upper I

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

△BCA∼△JIH

Answer 1

To determine the similarity statement between the two triangles, we should observe the correspondence of their angles.

Given:

• Triangle ABC:

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

• Triangle HIJ:

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

Now we can see how the angles correspond:

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

This means that the triangles are similar based on their angle measures.

To write this in the correct similarity statement, we can align them:

• Triangle ABC corresponds to Triangle HIJ as:
• \( A \) with \( I \)
• \( B \) with \( H \)
• \( C \) with \( J \)

Thus, the correct statement is: \( \triangle ABC \sim \triangle HIJ \).

So the final response is: \( \triangle ABC \sim \triangle HIJ \).