Question

△fgh and △ijk are shown below. which statement is true? △fgh is similar to △ijk. △fgh is not similar to △ijk.

Explanation:

Step1: Calculate the third angle of \(\triangle FGH\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle FGH\), if two angles are \(71^{\circ}\) and \(47^{\circ}\), then the third angle \(F\) is \(180-(71 + 47)=62^{\circ}\) (using the formula \(\angle A+\angle B+\angle C = 180^{\circ}\) for a triangle \(\triangle ABC\)).

Step2: Calculate the third angle of \(\triangle IJK\)

For \(\triangle IJK\), if two angles are \(62^{\circ}\) and \(71^{\circ}\), then the third angle \(K\) is \(180-(62 + 71)=47^{\circ}\) (using the formula \(\angle A+\angle B+\angle C = 180^{\circ}\) for a triangle \(\triangle ABC\)).

Step3: Check for similarity

Since \(\angle F=\angle I = 62^{\circ}\), \(\angle G=\angle J=71^{\circ}\), and \(\angle H=\angle K = 47^{\circ}\), by the AA (angle - angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), \(\triangle FGH\sim\triangle IJK\).

Answer:

\(\triangle FGH\) is similar to \(\triangle IJK\)