triangle cde is translated down and to the right, forming triangle cde. which congruency statement is correct?

$\delta dce \cong \delta dec$
$\delta dce \cong \delta dce$
$\delta edc \cong \delta cde$
$\delta edc \cong \delta ced$

Question

triangle cde is translated down and to the right, forming triangle cde. which congruency statement is correct?

$\delta dce \cong \delta dec$
$\delta dce \cong \delta dce$
$\delta edc \cong \delta cde$
$\delta edc \cong \delta ced$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Congruence", "Corresponding Parts" ], "new_concepts": [], "current_concepts": [ "Triangle Congruence", "Corresponding Parts", "Geometric Translations" ] } ## Identify corresponding vertices under translation $$ \begin{aligned} C &\to C' \ D &\to D' \ E &\to E' \end{aligned} $$ ## Match corresponding order in congruency statements $$ \begin{aligned} \Delta DCE &\cong \Delta D'C'E' \ \Delta EDC &\cong \Delta E'D'C' \end{aligned} $$ ## Evaluate the given options $$ \begin{aligned} \Delta DCE \cong \Delta D'E'C' &\quad (\text{Incorrect: } C \to E', E \to C') \ \Delta DCE \cong \Delta D'C'E' &\quad (\text{Correct: } D \to D', C \to C', E \to E') \ \Delta EDC \cong \Delta C'D'E' &\quad (\text{Incorrect: } E \to C', D \to D', C \to E') \ \Delta EDC \cong \Delta C'E'D' &\quad (\text{Incorrect: } E \to C', D \to E', C \to D') \end{aligned} $$

(A) $\Delta DCE \cong \Delta D'E'C'$

(B) $\Delta DCE \cong \Delta D'C'E'$

(C) $\Delta EDC \cong \Delta C'D'E'$

(D) $\Delta EDC \cong \Delta C'E'D'$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence" ] }

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Question

Explanation:

Identify corresponding vertices under translation

Match corresponding order in congruency statements

Evaluate the given options

Answer: