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 answer

The similarity statement that describes the relationship between the two triangles is that they are similar by the Angle-Angle (AA) similarity criterion.

In the first triangle, the angles are:

  • m∠A = 48°
  • m∠B = 17°
  • m∠C = 115°

In the second triangle, the angles are:

  • m∠H = 17°
  • m∠I = 48°
  • m∠J = 115°

Since both triangles have the same set of angles, they are similar. The similarity statement can be written as:

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

This indicates that triangle ABC is similar to triangle HIJ, since the corresponding angles are equal:

  • \(\angle A \leftrightarrow \angle I\)
  • \(\angle B \leftrightarrow \angle H\)
  • \(\angle C \leftrightarrow \angle J\)