Question
Angles of Similar Triangles Quick Check
2 of 52 of 5 Items
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
△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
triangle upper C upper A upper B tilde triangle upper J upper H upper I
△BAC∼△HIJ
Answers
GPT-4o mini
To determine the correct similarity statement between the two triangles, we need to check the corresponding angles.
The angles of the first triangle are:
- \( m∠A = 48^\circ \)
- \( m∠B = 17^\circ \)
- \( m∠C = 115^\circ \)
The angles of the second triangle are:
- \( m∠H = 17^\circ \)
- \( m∠I = 48^\circ \)
- \( m∠J = 115^\circ \)
Now, we can match the angles:
- \( m∠A = 48^\circ \) corresponds to \( m∠I = 48^\circ \)
- \( m∠B = 17^\circ \) corresponds to \( m∠H = 17^\circ \)
- \( m∠C = 115^\circ \) corresponds to \( m∠J = 115^\circ \)
Thus, the angles of the two triangles correspond as follows:
- A → I
- B → H
- C → J
This leads to the similarity statement:
\[
△ABC ∼ △HIJ
\]
So the correct response is:
**△ABC∼△HIJ**
The angles of the first triangle are:
- \( m∠A = 48^\circ \)
- \( m∠B = 17^\circ \)
- \( m∠C = 115^\circ \)
The angles of the second triangle are:
- \( m∠H = 17^\circ \)
- \( m∠I = 48^\circ \)
- \( m∠J = 115^\circ \)
Now, we can match the angles:
- \( m∠A = 48^\circ \) corresponds to \( m∠I = 48^\circ \)
- \( m∠B = 17^\circ \) corresponds to \( m∠H = 17^\circ \)
- \( m∠C = 115^\circ \) corresponds to \( m∠J = 115^\circ \)
Thus, the angles of the two triangles correspond as follows:
- A → I
- B → H
- C → J
This leads to the similarity statement:
\[
△ABC ∼ △HIJ
\]
So the correct response is:
**△ABC∼△HIJ**