Question

given
bc ≅ ad
diagram

congruence statement
△abc ≅ △

method

Explanation:

Step1: Analyze the given information

We have two right - angled triangles \(\triangle ABC\) and \(\triangle DCA\). We know that \(BC\cong AD\) (given), \(AC = AC\) (common side). Also, \(\angle BAC=\angle DCA = 90^{\circ}\)

Step2: Recall the HL (Hypotenuse - Leg) theorem

For right - angled triangles, if the hypotenuse and one leg of a right - angled triangle are congruent to the hypotenuse and one leg of another right - angled triangle, then the two right - angled triangles are congruent.

In \(\triangle ABC\) and \(\triangle DCA\), \(BC\) and \(AD\) are the hypotenuses (\(BC\cong AD\)), and \(AC\) is the common leg.

Answer:

Congruence Statement: \(\triangle ABC\cong\triangle DCA\)
Method: HL (Hypotenuse - Leg)