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°
?

△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

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

△CAB∼△JHI

Answer 1

To determine the correct similarity statement, we can use the angles of the triangles provided.

The first triangle has angles:

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

The second triangle has angles:

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

Triangles are similar if their corresponding angles are equal.

1. Comparing angles:
   • Angle \( A \) (48°) corresponds to angle \( I \) (48°).
   • Angle \( B \) (17°) corresponds to angle \( H \) (17°).
   • Angle \( C \) (115°) corresponds to angle \( J \) (115°).

All corresponding angles are equal.

2. Order of angles: We need to decide on the order of the letters for the similarity statement:

• The first triangle is often denoted \( \triangle ABC \), and through the matching of angles, we can pair them with the second triangle, which is \( \triangle HIJ \).

Thus, the appropriate similarity statement is: \[ \triangle ABC \sim \triangle HIJ \]

So the answer is: △ABC∼△HIJ.