Question

which postulate or theorem proves that \\( \triangle abc \\) and \\( \triangle cda \\) are congruent?
sas congruence postulate
asa congruence postulate
hl congruence theorem
aas congruence theorem

Explanation:

Step1: Analyze the given figure

Since \(ABCD\) is a rectangle, \(AB = CD\), \(AD=BC\), and \(\angle B=\angle D = 90^{\circ}\). Also, \(AC\) is the common hypotenuse for \(\triangle ABC\) and \(\triangle CDA\).

Step2: Recall the HL Congruence Theorem

The HL (Hypotenuse - Leg) Congruence Theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.
In \(\triangle ABC\) and \(\triangle CDA\), \(AC = AC\) (common hypotenuse) and \(AB = CD\) (legs of right - triangles \(\triangle ABC\) and \(\triangle CDA\))

Answer:

HL Congruence Theorem