in the diagram, $\overline{ab} \cong \overline{ad}$ and $\overline{bc} \cong \overline{de}$. what additional information is necessary to prove that $\delta abc \cong \delta ade$, using the sas congruence theorem?

$\bigcirc \overline{ac} \cong \overline{ae}$
$\bigcirc \overline{ac} \cong \overline{ad}$
$\bigcirc \angle abc \cong \angle ade$
$\bigcirc \angle bac \cong \angle dae$

Question

in the diagram, $\overline{ab} \cong \overline{ad}$ and $\overline{bc} \cong \overline{de}$. what additional information is necessary to prove that $\delta abc \cong \delta ade$, using the sas congruence theorem?

$\bigcirc \overline{ac} \cong \overline{ae}$
$\bigcirc \overline{ac} \cong \overline{ad}$
$\bigcirc \angle abc \cong \angle ade$
$\bigcirc \angle bac \cong \angle dae$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "SAS Congruence Theorem" ], "new_concepts": [], "current_concepts": [ "SAS Congruence Theorem", "Triangle Congruence" ] } ## Identify the given congruent sides $$ \begin{aligned} &\overline{AB} \cong \overline{AD} \ &\overline{BC} \cong \overline{DE} \end{aligned} $$ ## Determine the required angle for SAS congruence $$ \begin{aligned} &\text{For } \Delta ABC \text{ and } \Delta ADE: \ &\text{Sides: } AB \text{ and } BC \implies \text{Included angle: } \angle ABC \ &\text{Sides: } AD \text{ and } DE \implies \text{Included angle: } \angle ADE \end{aligned} $$ ## State the necessary congruence relation $$ \angle ABC \cong \angle ADE $$

(A) $\overline{AC} \cong \overline{AE}$

(B) $\overline{AC} \cong \overline{AD}$ (C) $\angle ABC \cong \angle ADE$

(D) $\angle BAC \cong \angle DAE$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given congruent sides

Determine the required angle for SAS congruence

State the necessary congruence relation

Answer: