Question

yes, by hl
yes, by sas
yes, by aas
no, this is the ssa one!!
are these triangles congruent?

Explanation:

Step1: Analyze the given information

We have two triangles \( \triangle ABD \) and \( \triangle CBD \). We know that \( AB = CB \) (marked with one - cross), \( BD=BD \) (common side), and \( \angle ADB=\angle CDB = 90^{\circ}\) (right - angles).

Step2: Recall the congruence criteria

The Hypotenuse - Leg (HL) criterion for right - triangles states that if the hypotenuse and one leg of a right - triangle are equal to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent. Here, \( BD\) is the common leg, \( AB = CB\) (hypotenuses of right - triangles \( \triangle ABD\) and \( \triangle CBD\))

Answer:

Yes, by HL