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

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

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

△CAB∼△JHI

Answer 1

To determine the similarity between the two triangles based on their angles, we can use the Angle-Angle (AA) similarity criterion. Two triangles are similar if their corresponding angles are equal.

For triangle \( \triangle ABC \):

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

For triangle \( \triangle HIJ \):

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

Now, let's match the 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 all corresponding angles are equal, we can conclude that the two triangles are similar.

Among the given response options, \( \triangle ABC \sim \triangle HIJ \) correctly represents the relationship, matching the letters according to their angle measures.

So the correct similarity statement is:

\( \triangle ABC \sim \triangle HIJ \)