Question

△cde and △fgh are shown below. 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: Calculate angles in \(\triangle CDE\)

Since \(\triangle CDE\) is isosceles (\(CD = CE\)), the base - angles are equal. Let the base - angles be \(x\). Using the angle - sum property of a triangle (\(x + x+86^{\circ}=180^{\circ}\)), we get \(2x = 180^{\circ}- 86^{\circ}=94^{\circ}\), so \(x = 47^{\circ}\).

Step2: Calculate angles in \(\triangle FGH\)

Since \(\triangle FGH\) is isosceles (\(FG = FH\)), the base - angles are equal. Let the base - angles be \(y\). Using the angle - sum property of a triangle (\(y + y + 44^{\circ}=180^{\circ}\)), we get \(2y=180^{\circ}-44^{\circ} = 136^{\circ}\), so \(y = 68^{\circ}\).

Step3: Check for 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, the triangles are not similar.

Answer:

\(\triangle CDE\) is not similar to \(\triangle FGH\).