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: Analyze triangle \( \triangle DEF \)

In \( \triangle DEF \), two sides are equal (marked with the same tick), so \( \triangle DEF \) is an isosceles triangle. The base angles are equal. Let the equal angles be \( x \). Using the angle - sum property of a triangle (\( x + x+56^{\circ}=180^{\circ}\)), we get \( 2x = 124^{\circ}\), \( x = 62^{\circ}\).

Step2: Analyze triangle \( \triangle GHI \)

In \( \triangle GHI \), two sides are equal (marked with the same tick), so \( \triangle GHI \) is an isosceles triangle. The base angles are equal. Let the equal angles be \( y \). Using the angle - sum property of a triangle (\( y + y + 56^{\circ}=180^{\circ}\)), we get \( 2y=124^{\circ}\), \( y = 62^{\circ}\).

Step3: Check similarity

Since the corresponding angles of \( \triangle DEF \) and \( \triangle GHI \) are equal (\(56^{\circ}=56^{\circ}\), \(62^{\circ}=62^{\circ}\)), by the AA (angle - angle) similarity criterion, \( \triangle DEF\sim\triangle GHI \).

Answer:

\( \triangle DEF\) is similar to \( \triangle GHI \)