Question

en el banco de artículos se enumeranalgunas etiquetas importantes para lasecciones de la imagen a continuación.para obtener más información sobre lasetiquetas, algunas tienen más detallesdisponibles al hacer clic en ellas. arrastre ysuelte cada etiqueta en el áreacorrespondiente que identifica en laimagen.dado: d es el punto medio del segmentobf, segmento bc || segmento fedemostrar: △bdc ≅ △fde

Explanation:

Step1: Fill in the second statement

Since \(D\) is the mid - point of segment \(BF\), by the definition of mid - point, \(BD = FD\). So the second statement is \(BD=FD\).

Step2: Fill in the reason for \(\angle BDC\cong\angle FDE\)

\(\angle BDC\) and \(\angle FDE\) are vertical angles. By the property that vertical angles are congruent, the reason for \(\angle BDC\cong\angle FDE\) is "vertical angles are congruent".

Step3: Fill in the reason for \(\triangle BDC\cong\triangle FDE\)

We know that \(BC\parallel EF\), so \(\angle B=\angle F\) (alternate interior angles of parallel lines). We have \(BD = FD\) (from the mid - point definition), \(\angle BDC=\angle FDE\) (vertical angles). By the Angle - Side - Angle (ASA) congruence criterion, \(\triangle BDC\cong\triangle FDE\).

Answer:

Statements	Reasons
\(BD = FD\)	definition of midpoint
\(\angle BDC\cong\angle FDE\)	vertical angles are congruent
\(\angle B=\angle F\)	alternate interior angles of \(\parallel\) lines are congruent
\(\triangle BDC\cong\triangle FDE\)	Angle - Angle - Side (\(ASA\))