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

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

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

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

△ABC∼△HIJ

Answer 1

To determine which similarity statement describes the relationship between the two triangles based on their angle measures, we first note the angles of each triangle:

For triangle CAB:

• m∠A = 48°
• m∠B = 17°
• m∠C = 115°

For triangle JHI:

• m∠H = 17°
• m∠I = 48°
• m∠J = 115°

Now, let's list the angle measures of each triangle in a consistent order. The angles can be matched as follows:

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

Since the angles from each triangle match in size, the triangles are similar by the Angle-Angle (AA) similarity postulate.

Now, we can look at the similarity statements given in the options:

1. △CAB∼△JHI (matches as A=I, B=H, C=J)
2. △BCA∼△JIH (matches as B=H, C=I, A=J)
3. △BAC∼△HIJ (matches as B=H, A=I, C=J)
4. △ABC∼△HIJ (matches as A=I, B=H, C=J)

The correct similarity statement based on our order and position would be △CAB∼△JHI because angles A, B, and C correspond directly to angles I, H, and J respectively based on their positions.

Thus, the answer is: △CAB∼△JHI.