Question

which of the following statements must be true?
∠c is a right angle.
∠d and ∠e are congruent
∠cab and ∠cde are congruent.
ad and ca are equal length.

Explanation:

Step1: Identify similar - triangles concept

If two triangles have their corresponding angles equal, they are similar. In the given figure, \(\triangle CAB\) and \(\triangle CDE\) share the same angle \(\angle C\) and the lines \(AB\) and \(DE\) are likely parallel (implied by the triangle - within - triangle structure). If \(AB\parallel DE\), then the corresponding angles formed by the transversal \(CE\) are equal. Specifically, \(\angle CAB\) and \(\angle CDE\) are corresponding angles.

Step2: Analyze each option

• Option 1: There is no indication that \(\angle C\) is a right - angle.
• Option 2: There is no information to suggest that \(\angle D\) and \(\angle E\) are congruent.
• Option 3: Since \(AB\parallel DE\) (assumed from the structure), by the property of corresponding angles for parallel lines cut by a transversal, \(\angle CAB\) and \(\angle CDE\) are congruent.
• Option 4: There is no evidence that \(AD\) and \(CA\) are of equal length.

Answer:

\(\angle CAB\) and \(\angle CDE\) are congruent.