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

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Geometric Proofs", "Substitution Property" ], "current_concepts": [ "Geometric Proofs", "Substitution Property", "Linear Pair Postulate" ] } ## Identificar la relación de igualdad $$ \begin{aligned} &m\angle3 + m\angle4 = 180^\circ \ &m\angle8 + m\angle5 = 180^\circ \end{aligned} $$ ## Aplicar la propiedad de sustitución $$ m\angle3 + m\angle4 = m\angle8 + m\angle5 $$ ## Determinar la razón correspondiente La justificación para igualar dos expresiones que son iguales a una misma cantidad ($180^\circ$) es la **Substitution Property of Equality**. The correct reason for statement 4) is Substitution Property of Equality. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Geometric Proofs" ] }

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Question

Explanation:

Identificar la relación de igualdad

Aplicar la propiedad de sustitución

Determinar la razón correspondiente

Answer: