Question

1. in the figure segment $ac \cong$ segment $fd$, segment $ab \parallel$ segment $de$, and segment $ac \parallel fd$. determine which postulate can be used to prove $\triangle abc \cong \triangle def$. choose from sss, sas, asa, aas, or hl.

sas

Explanation:

Step1: Identify alternate interior angles

Since $AB \parallel DE$, $\angle BAC = \angle EDF$ (alternate interior angles).

Step2: Identify given congruent sides

We know $\overline{AC} \cong \overline{FD}$.

Step3: Identify second pair of angles

Since $AC \parallel FD$, $\angle ACB = \angle DFE$ (alternate interior angles).

Step4: Match to congruence postulate

We have two pairs of congruent angles and a pair of congruent included sides, which fits the ASA postulate.

Answer:

ASA