Question

which statement is true?
△cde is similar to △fgh.
△cde is not similar to △fgh.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find the third angle of $\triangle CDE$

In an isosceles triangle $\triangle CDE$ (since two sides are equal), the sum of angles in a triangle is $180^{\circ}$. Let the other two angles be $x$. We have $86^{\circ}+2x = 180^{\circ}$. Solving for $x$: $2x=180^{\circ}- 86^{\circ}=94^{\circ}$, so $x = 47^{\circ}$.

Step2: Find the third angle of $\triangle FGH$

In an isosceles triangle $\triangle FGH$ (since two sides are equal), the sum of angles in a triangle is $180^{\circ}$. Let the other two angles be $y$. We have $44^{\circ}+2y = 180^{\circ}$. Solving for $y$: $2y=180^{\circ}-44^{\circ}=136^{\circ}$, so $y = 68^{\circ}$.

Step3: Check similarity

For two triangles to be similar, their corresponding angles must be equal. The angles of $\triangle CDE$ are $86^{\circ},47^{\circ},47^{\circ}$ and the angles of $\triangle FGH$ are $44^{\circ},68^{\circ},68^{\circ}$. Since the angles are not equal.

Answer:

$\triangle CDE$ is not similar to $\triangle FGH$.