Question

error analysis in exercises 15 and 16, describe and correct the error.

1. $\triangle jkl \cong \triangle fhg$ by the asa congruence theorem.
2. $\triangle qrs \cong \triangle vwx$ by the aas congruence theorem.

Explanation:

For Exercise 15:

1. Error Description: The congruence statement mismatches the corresponding parts, and the wrong congruence theorem was cited. In $\triangle JKL$, the marked side $JK$ is between the two marked angles, making it ASA. However, $\triangle FHG$ has the marked side $GF$ opposite the unmarked angle, so the correct correspondence is $\triangle JKL \cong \triangle HGF$, not $\triangle FHG$.
2. Correction: The triangles are congruent by the ASA Congruence Theorem, with the correct congruence statement $\triangle JKL \cong \triangle HGF$.

For Exercise 16:

1. Error Description: The congruence statement misaligns corresponding parts, and the wrong theorem was cited. In $\triangle QRS$, the marked side $QR$ is between the marked angle at $Q$ and the marked angle at $R$. In $\triangle VWX$, the marked side $WX$ is between the marked angle at $W$ and the marked angle at $V$. This fits ASA, not AAS, and the correct correspondence is $\triangle QRS \cong \triangle VWX$.
2. Correction: The triangles are congruent by the ASA Congruence Theorem, with the correct congruence statement $\triangle QRS \cong \triangle VWX$.

Answer:

Exercise 15:

Error: Incongruent triangle correspondence and misstated theorem.
Correction: $\triangle JKL \cong \triangle HGF$ by the ASA Congruence Theorem.

Exercise 16:

Error: Misidentified congruence theorem.
Correction: $\triangle QRS \cong \triangle VWX$ by the ASA Congruence Theorem.