Question

chapter 5: proving triangle congruence by sss > section exercises 5.5 > exercise 19
$\triangle tuv cong \triangle xyz$ by the sss congruence theorem.

there is not enough information to classify the triangles congruent by sss

in naming any triangle, the letters should always represent a counter - clockwise movement about the vertices of the triangle

there is more than way that the vertices of the triangles correspond as congruent triangles.

the order of the letters in the congruence statement should reflect the corresponding vertices of the congruent triangles.

correct the error

$\triangle tuv cong \triangle xyz$ by the sss congruence theorem

$\triangle tuv cong \triangle zyx$ by the sss congruence theorem

$\triangle tuv cong \triangle xyz$ by the sas congruence theorem

$\triangle tuv cong \triangle zxy$ by the sas congruence theorem

Explanation:

First, identify the error in the original congruence statement: the vertex order does not match the corresponding congruent sides. The side markings show that side $TU$ corresponds to $ZY$, $UV$ corresponds to $YX$, and $TV$ corresponds to $ZX$. So the congruence statement must reflect this correct vertex correspondence. Then, the correct reason is still SSS since all three pairs of sides are congruent.

Answer:

Correct error explanation option: The order of the letters in the congruence statement should reflect the corresponding vertices of the congruent triangles.
Corrected congruence statement: $\triangle TUV \cong \triangle ZYX$ by the SSS Congruence Theorem.