Question

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

Explanation:

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

The sum of angles in a triangle is $180^{\circ}$.
For $\triangle CDE$, let the third angle be $\angle D$.
$\angle D=180^{\circ}-(48^{\circ} + 80^{\circ})=180^{\circ}-128^{\circ}=52^{\circ}$

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

For $\triangle FGH$, let the third angle be $\angle H$.
$\angle H=180^{\circ}-(48^{\circ}+62^{\circ})=180^{\circ}-110^{\circ}=70^{\circ}$

Since the angles of $\triangle CDE$ ($48^{\circ},80^{\circ},52^{\circ}$) and $\triangle FGH$ ($48^{\circ},62^{\circ},70^{\circ}$) are not equal, the triangles are not similar.

Answer:

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