statements | reasons
$abcd$ is a square. | given
$\overline{ab} \cong \overline{bc}$ | definition of a square
$\overline{be} \cong \overline{be}$ | dropdown: substitution, reflexive, transitive, symmetric
$\overline{bd}$ bisects $\overline{ac}$ | property
$\overline{ae} \cong \overline{ce}$ | def. of a segment bisector
$\delta abe \cong \delta cbe$ | dropdown
$\angle aeb \cong \angle bec$ | dropdown
$m\angle aeb \cong m\angle bec$ | def. of congruent angles
$\angle aeb$ and $\angle bec$ are a linear pair | def. of linear pairs
$\angle aeb$ and $\angle bec$ are supplementary | linear pair postulate
$m\angle aeb + m\angle bec = 180^\circ$ | def. of supplementary angles
$m\angle aeb + m\angle aeb = 180^\circ$ | dropdown property
$2 \cdot m\angle aeb = 180^\circ$ | simplify
$m\angle aeb = 90^\circ$ | dropdown property
$\overline{ac} \perp \overline{db}$ | def. of perpendicular lines

Question

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Proofs", "Triangle Congruence", "Substitution Property", "Linear Pair Postulate" ], "new_concepts": [ "Reflexive Property", "CPCTC", "Division Property of Equality" ], "current_concepts": [ "Geometric Proofs", "Triangle Congruence", "Substitution Property", "Reflexive Property", "CPCTC", "Division Property of Equality" ] } ## Identificar la razón para $\overline{BE} \cong \overline{BE}$ $$ \text{Propiedad reflexiva (Reflexive)} $$ ## Identificar la razón para $\triangle ABE \cong \triangle CBE$ $$ \text{Postulado de congruencia LLL (SSS)} $$ ## Identificar la razón para $\angle AEB \cong \angle BEC$ $$ \text{CPCTC (Partes correspondientes de triángulos congruentes son congruentes)} $$ ## Identificar la propiedad para $m\angle AEB + m\angle AEB = 180^\circ$ $$ \text{Propiedad de sustitución (Substitution)} $$ ## Identificar la propiedad para $m\angle AEB = 90^\circ$ $$ \text{Propiedad de división de la igualdad (Division)} $$ | No. | Declaración / Statement | Razón / Reason | |---|---|---| | 1 | $\overline{BE} \cong \overline{BE}$ | Reflexive | | 2 | $\triangle ABE \cong \triangle CBE$ | SSS | | 3 | $\angle AEB \cong \angle BEC$ | CPCTC | | 4 | $m\angle AEB + m\angle AEB = 180^\circ$ | Substitution | | 5 | $m\angle AEB = 90^\circ$ | Division | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Geometric Proofs" ] }

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QUESTION IMAGE

Question

Explanation:

Identificar la razón para \(\overline{BE} \cong \overline{BE}\)

Identificar la razón para \(\triangle ABE \cong \triangle CBE\)

Identificar la razón para \(\angle AEB \cong \angle BEC\)

Identificar la propiedad para \(m\angle AEB + m\angle AEB = 180^\circ\)

Identificar la propiedad para \(m\angle AEB = 90^\circ\)

Answer:

No.	Declaración / Statement	Razón / Reason
2	\(\triangle ABE \cong \triangle CBE\)	SSS
3	\(\angle AEB \cong \angle BEC\)	CPCTC
4	\(m\angle AEB + m\angle AEB = 180^\circ\)	Substitution
5	\(m\angle AEB = 90^\circ\)	Division