Question

which congruence theorem can be used to prove \\( \triangle bda \cong \triangle dbc \\)?

Explanation:

Step1: Identify the right - angled triangles

We have \(\triangle BDA\) and \(\triangle DBC\) which are right - angled triangles (as indicated by the right - angle marks).

Step2: Check the hypotenuse and leg

For right - angled triangles, the Hypotenuse - Leg (HL) congruence theorem states that if the hypotenuse and a leg of one right - angled triangle are equal to the hypotenuse and a leg of another right - angled triangle, then the two triangles are congruent.
In \(\triangle BDA\) and \(\triangle DBC\), we can assume (from the markings in the diagram, if we consider the equal - length markings as hypotenuse and a leg) that the hypotenuse and a leg are equal.
So, the HL (Hypotenuse - Leg) congruence theorem can be used to prove \(\triangle BDA\cong\triangle DBC\).

Answer:

A. HL