Question

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

Explanation:

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

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle EFD\), if two angles are \(53^{\circ}\) and \(63^{\circ}\), then the third angle \(\angle FED=180^{\circ}-(53^{\circ} + 63^{\circ})=180^{\circ}-116^{\circ} = 64^{\circ}\)

Step2: Check for similarity using AA (Angle - Angle) criterion

In \(\triangle BCD\), \(\angle B = 64^{\circ}\). In \(\triangle EFD\), \(\angle FED=64^{\circ}\). Also, \(\angle D\) is common to both \(\triangle BCD\) and \(\triangle EFD\). By AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), \(\triangle BCD\sim\triangle EFD\)

Answer:

\(\triangle BCD\) is similar to \(\triangle EFD\)