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

Step2: Find angles of $\triangle GHI$

Since $\triangle GHI$ has two equal sides (marked with two ticks), it is isosceles. Let the base - angles be $y$. Using the angle - sum property of a triangle ($y + y + 56^{\circ}=180^{\circ}$), we get $2y=180^{\circ}-56^{\circ}=124^{\circ}$, so $y = 62^{\circ}$. But wait, no! Wait, $\triangle GHI$: the vertex angle is calculated as follows. Since the two equal sides are not adjacent to the $56^{\circ}$ angle. Let the vertex angle be $z$. Using the angle - sum property of a triangle ($56^{\circ}+56^{\circ}+z = 180^{\circ}$). Wait, no, $\triangle GHI$: the two equal sides (marked with two ticks) mean that the angles opposite to them are equal. The angle adjacent to the side with two ticks: if we use the angle - sum property of a triangle. For $\triangle DEF$: angles are $56^{\circ},62^{\circ},62^{\circ}$. For $\triangle GHI$: since the two equal sides (marked with two ticks) - the angles opposite to them are equal. Let's re - calculate.
For $\triangle DEF$: it is isosceles with vertex angle $\angle D = 56^{\circ}$. Using the formula for the base - angles of an isosceles triangle $\theta=\frac{180^{\circ}-\alpha}{2}$, where $\alpha$ is the vertex angle. So $\angle E=\angle F=\frac{180 - 56}{2}=62^{\circ}$
For $\triangle GHI$: it is isosceles with base - angle $\angle H = 56^{\circ}$. Then the vertex angle $\angle G=180^{\circ}-2\times56^{\circ}=180^{\circ}-112^{\circ}=68^{\circ}$

Since the angles of $\triangle DEF$ ($56^{\circ},62^{\circ},62^{\circ}$) and the angles of $\triangle GHI$ ($56^{\circ},56^{\circ},68^{\circ}$) are not equal.

Answer:

$\triangle DEF$ is not similar to $\triangle GHI$.