Question

given ( abcong cd ) and ( bccong ad ). prove that ( \triangle abccong\triangle cda ).

Explanation:

Step1: Identify right angles

In the figure, $\angle B$ and $\angle D$ are right angles. So, $\angle B\cong\angle D$.

Step2: Use Hypotenuse - Leg (HL) criterion

For right - angled triangles $\triangle ABC$ and $\triangle CDA$, we have $AB\cong CD$ (given), $BC\cong AD$ (given), and $\angle B\cong\angle D = 90^{\circ}$.
By the Hypotenuse - Leg (HL) congruence criterion 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.

Answer:

$\triangle ABC\cong\triangle CDA$ by the Hypotenuse - Leg (HL) congruence criterion.