which of the following are congruent? select four correct answers.

$\delta stv$ and $\delta utv$
$\overline{st}$ and $\overline{tv}$
$\angle stv$ and $\angle svt$
$\overline{uv}$ and $\overline{sv}$
$\angle u$ and $\angle s$
$\angle tvu$ and $\angle svt$

Question

which of the following are congruent? select four correct answers.

$\delta stv$ and $\delta utv$
$\overline{st}$ and $\overline{tv}$
$\angle stv$ and $\angle svt$
$\overline{uv}$ and $\overline{sv}$
$\angle u$ and $\angle s$
$\angle tvu$ and $\angle svt$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_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" ] } ## Identify given congruent parts from the figure $$ \begin{aligned} &ST = UT \quad (\text{single tick marks}) \ &SV = UV \quad (\text{double tick marks}) \ &TV = TV \quad (\text{reflexive property}) \end{aligned} $$ ## Establish triangle congruence $$ \begin{aligned} &\Delta STV \cong \Delta UTV \quad (\text{by SSS Congruence Postulate}) \end{aligned} $$ ## Determine corresponding congruent parts (CPCTC) $$ \begin{aligned} &\angle U \cong \angle S \ &\angle STV \cong \angle UTV \ &\angle TVU \cong \angle TVS \quad (\text{or } \angle SVT) \ &\overline{ST} \cong \overline{UT} \ &\overline{SV} \cong \overline{UV} \end{aligned} $$

[x] $\Delta STV$ and $\Delta UTV$

[ ] $\overline{ST}$ and $\overline{TV}$

[ ] $\angle STV$ and $\angle SVT$

[x] $\overline{UV}$ and $\overline{SV}$

[x] $\angle U$ and $\angle S$

[x] $\angle TVU$ and $\angle SVT$

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

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QUESTION IMAGE

Question

Explanation:

Identify given congruent parts from the figure

Establish triangle congruence

Determine corresponding congruent parts (CPCTC)

Answer: