statements reasons
1) $l \parallel n$ given
2) $m\angle 3 + m\angle 4 = 180^{\circ}$ linear pair postulate
3) $m\angle 8 + m\angle 5 = 180^{\circ}$ linear pair postulate
4) $m\angle 3 + m\angle 4 = m\angle 8 + m\angle 5$ vertical angles theorem
5) $\angle 4 \cong \angle 8$ co
6) $m\angle 2 = m\angle 8$ d
7) $m\angle 3 + m\angle 8 = m\angle 8 + m\angle 5$
8) $m\angle 3 = m\angle 5$ subtraction property of equality
9) $\angle 3 \cong \angle 5$ definition of congruent angles

Question

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Proofs", "Substitution Property" ], "new_concepts": [ "Transitive Property of Equality" ], "current_concepts": [ "Geometric Proofs", "Substitution Property", "Vertical Angles", "Linear Pair Postulate" ] } ## Identificar la relación en el paso 4 $$ \begin{aligned} &m\angle 3 + m\angle 4 = 180^\circ \quad \text{y} \quad m\angle 8 + m\angle 5 = 180^\circ \ &m\angle 3 + m\angle 4 = m\angle 8 + m\angle 5 \end{aligned} $$ ## Determinar la propiedad matemática aplicada $$ \text{Propiedad de sustitución de la igualdad (Substitution Property of Equality)} $$ ## Identificar la congruencia en el paso 6 $$ \begin{aligned} &\text{Paso 5: } \angle 4 \cong \angle 8 \implies m\angle 4 = m\angle 8 \ &\text{Sustituyendo en el Paso 4: } m\angle 3 + m\angle 8 = m\angle 8 + m\angle 5 \end{aligned} $$ Para la razón del paso 4: **Substitution Property of Equality** Para el valor del paso 6: **$4$** { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Geometric Proofs" ] }

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Question

Explanation:

Identificar la relación en el paso 4

Determinar la propiedad matemática aplicada

Identificar la congruencia en el paso 6

Answer: