Answer:
Option B is correct
The congruence theorem HA prove the triangles are congruent.
Explanation:
First labelled the given picture as shown in the attachment below:
We need to show that triangle ABC and ABD are congruent.
Hypotenuse angle theorem(HA) states that if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.
In \(\triangle ABC\) and \(\triangle ABD\)
\(AC = AD\) [Hypotenuse] {Given}
\(m\angle ABC = m\angle ABD = 90^{\circ}\) [Given]
\(m \angle ACB = m\angle ADB\) [acute angle]
then, by the HA Congruence theorem ;
\(\triangle ABC \cong \triangle ABD\)
Therefore, the triangle in the given figure are congruent by HA theorem
