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

△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 between the two triangles based on their angles, we first analyze the angles in each triangle.

For triangle ABC:

• m∠A = 48°
• m∠B = 17°
• m∠C = 115°

For triangle HIJ:

• m∠H = 17°
• m∠I = 48°
• m∠J = 115°

The order of the angles matters in determining the similarity statement. First, let's see how we can match the angles:

• m∠A = 48° matches with m∠I = 48°
• m∠B = 17° matches with m∠H = 17°
• m∠C = 115° matches with m∠J = 115°

From this matching, we conclude the angles correspond in the order:

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

From this angle correspondence, we conclude:

• Triangle ABC is similar to triangle HIJ.

Now we can express this as:

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

Thus, the correct similarity statement is:

△ABC∼△HIJ