Question

1. error analysis describe and correct the error in finding the length of bc. because ∠a ≅ ∠c, ac ≅ bc. so, bc = 6.

Explanation:

Step1: Identify the Error

In a triangle, if two angles are congruent, the sides opposite those angles are congruent (Isosceles Triangle Theorem). Here, $\angle A \cong \angle C$. The side opposite $\angle A$ is $BC$, and the side opposite $\angle C$ is $AB$.

Step2: Correct the Relationship

So, by the Isosceles Triangle Theorem, $BC \cong AB$, not $BC \cong AC$. Given $AB = 5$, so $BC = 5$.

Answer:

The error is misapplying the Isosceles Triangle Theorem (matching the wrong sides to the congruent angles). The correct length of $BC$ is $5$ (since $BC$ is opposite $\angle A$ and $AB$ is opposite $\angle C$, so $BC = AB = 5$).