Question

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

Explanation:

Step1: Find angles of \(\triangle DEF\)

Since \(DE = DF\) in \(\triangle DEF\), it is an isosceles triangle. Let \(\angle E=\angle F\). Using the angle - sum property of a triangle (\(\angle D+\angle E+\angle F = 180^{\circ}\)), and \(\angle D = 56^{\circ}\), we have \(2\angle E=180^{\circ}- 56^{\circ}=124^{\circ}\), so \(\angle E=\angle F = 62^{\circ}\).

Step2: Find angles of \(\triangle GHI\)

Since \(GH = GI\) in \(\triangle GHI\), it is an isosceles triangle. Let \(\angle H=\angle I = 56^{\circ}\). Using the angle - sum property of a triangle (\(\angle G+\angle H+\angle I=180^{\circ}\)), we have \(\angle G=180^{\circ}-(56^{\circ}+56^{\circ}) = 68^{\circ}\).

Step3: Check similarity

For two triangles to be similar, their corresponding angles must be equal. In \(\triangle DEF\) the angles are \(56^{\circ},62^{\circ},62^{\circ}\) and in \(\triangle GHI\) the angles are \(68^{\circ},56^{\circ},56^{\circ}\). Corresponding angles are not equal.

Answer:

\(\triangle DEF\) is not similar to \(\triangle GHI\).