Question

Which similarity statement describes the relationship between a triangle with angles m∠A=48° , 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 △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 triangle upper C upper A upper B tilde triangle upper J upper H upper I △BCA∼△JIH

Answer 1

To establish the similarity between triangles based on their angles, we categorize the triangles based on the measures of their angles.

For triangle ABC, we have:

• m∠A = 48°
• m∠B = 17°
• m∠C = 115°

For triangle HIJ, we have:

• m∠H = 17°
• m∠I = 48°
• m∠J = 115°

Now, we can see that:

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

The angles of triangle ABC correspond to the angles of triangle HIJ in the same order (A corresponds to I, B to H, C to J), meaning these triangles are similar.

Thus, the similarity can be expressed as:

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

So, the correct response is: △ABC∼△HIJ