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° ?

Answer 1

To describe the relationship between the two triangles based on their angles, we can utilize the similarity criterion for triangles. Two triangles are similar if their corresponding angles are equal.

For the triangles you provided:

- Triangle 1 has angles:
- \( m∠A = 48° \)
- \( m∠B = 17° \)
- \( m∠C = 115° \)

- Triangle 2 has angles:
- \( m∠H = 17° \)
- \( m∠I = 48° \)
- \( m∠J = 115° \)

Now let us arrange the angles of both triangles in a standard order:

For Triangle 1:
- \( 48° \) (A), \( 17° \) (B), \( 115° \) (C)

For Triangle 2:
- \( 17° \) (H), \( 48° \) (I), \( 115° \) (J)

If we reorder Triangle 2 to correspond to Triangle 1, we find the following pairs of equal angles:

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

Since all corresponding angles are equal, we can conclude that the two triangles are similar.

Thus, the similarity statement can be given as:

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

This states that Triangle ABC is similar to Triangle HIJ.