Find the value of x and y that make these triangles congruent by hl.

 the correct option is (A) x = y = 2.

Step-by-step explanation:  We are given to find the values of x and y that makes the triangles in the figure congruent by HL.

From the figure, we note that

triangles ABC and AED are right-angled triangles with hypotenuse AC, AD and one congruent side BC, ED.

Also, AC = 2x + 3, AD = 3y+1, BC = x  and  ED = y.

Since the triangles are congruent by HL postulate, so we must have

Substituting the value of x from equation (i) in equation (ii), we get

So, from equation (i), we arrive at

x = y = 2.

Thus, the correct option is (A).