Question

△fgh and △ijk are shown below. which statement is true? △fgh is similar to △ijk. △fgh is not similar to △ijk. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find ∠F in △FGH

Sum of angles in triangle is $180^\circ$.
$\angle F = 180^\circ - 71^\circ - 47^\circ = 62^\circ$

Step2: Find ∠K in △IJK

Sum of angles in triangle is $180^\circ$.
$\angle K = 180^\circ - 62^\circ - 71^\circ = 47^\circ$

Step3: Compare triangle angles

△FGH angles: $71^\circ, 47^\circ, 62^\circ$; △IJK angles: $71^\circ, 62^\circ, 47^\circ$. All corresponding angles are equal.

Answer:

△FGH is similar to △IJK.