find the values of x and y that make these triangles congruent by the hl theorem x=2,y=3 x=-2,y=3x=3,y=2x=4,y=8

Answer:The correct option is x=3 , y=2Step-by-step explanation:According to the HL theorem if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle then the triangles are congruent.By using this theorem we can set up the system of equations as follows:x=y+1 ...(1) 2x+3= 3y + 3 ..(2)Now we will plug the value y+1 of equation 1 in equation 2.2x+3 = 3y+32(y+1)+3=3y+32y+2+3=3y+32y+5=3y+3Now combine the like terms:5-3=3y-2y2=yy=2Now plug the value y=2 in equation 1.x=y+1x=2+1x=3Thus the values of(x.y) are{(2,3)}Therefore the correct option is x=3 , y=2 .....