in the diagram, $\overline{kl} \cong \overline{nr}$ and $\overline{jl} \cong \overline{mr}$. what additional information is needed to show $\delta jkl \cong \delta mnr$ by sas?

$\bigcirc$ $\angle j \cong \angle m$
$\bigcirc$ $\angle l \cong \angle r$
$\bigcirc$ $\angle k \cong \angle n$
$\bigcirc$ $\angle r \cong \angle k$

Question

in the diagram, $\overline{kl} \cong \overline{nr}$ and $\overline{jl} \cong \overline{mr}$. what additional information is needed to show $\delta jkl \cong \delta mnr$ by sas?

$\bigcirc$ $\angle j \cong \angle m$
$\bigcirc$ $\angle l \cong \angle r$
$\bigcirc$ $\angle k \cong \angle n$
$\bigcirc$ $\angle r \cong \angle k$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "SAS Congruence Postulate" ], "new_concepts": [], "current_concepts": [ "SAS Congruence Postulate", "Triangle Congruence Proofs" ] } ## Identify the given congruent sides Using the *SAS Congruence Postulate* knowledge point $$ \begin{aligned} &\overline{KL} \cong \overline{NR} \ &\overline{JL} \cong \overline{MR} \end{aligned} $$ ## Determine the required included angles Using the *SAS Congruence Postulate* knowledge point $$ \begin{aligned} &\text{For } \Delta JKL, \text{ the included angle between } \overline{KL} \text{ and } \overline{JL} \text{ is } \angle L.\ &\text{For } \Delta MNR, \text{ the included angle between } \overline{NR} \text{ and } \overline{MR} \text{ is } \angle R.\ &\text{Therefore, we need: } \angle L \cong \angle R. \end{aligned} $$

(A) $\angle J \cong \angle M$

(B) $\angle L \cong \angle R$

(C) $\angle K \cong \angle N$

(D) $\angle R \cong \angle K$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given congruent sides

Determine the required included angles

Answer: