Question

question
given: \\(\overline{ca}\\) bisects \\(\angle bad\\) and \\(\overline{ad} \cong \overline{ab}\\).
prove: \\(\triangle abc \cong \triangle adc\\).

step	statement	reason
try	\\(\triangle \square \cong \triangle \square\\)	sas

(image of a quadrilateral with vertices b, c, a (at the bottom), and d, with diagonal ca and side ab marked congruent to ad)

Explanation:

Step1: Analizar el ángulo bisectado

Dado que $\overline{CA}$ bisecta $\angle BAD$, entonces $\angle BAC \cong \angle DAC$.

Step2: Identificar lados y ángulo

Tenemos $\overline{AD} \cong \overline{AB}$ (dado), $\angle BAC \cong \angle DAC$ (por bisectriz) y $\overline{CA} \cong \overline{CA}$ (lado común). Entonces, por SAS, $\triangle ABC \cong \triangle ADC$.

Answer:

$\triangle ABC \cong \triangle ADC$