Find the values of x and y that make these triangles congruent by the HL theorem

A. x = 3, y = 2

Step-by-step explanation:

The hypotenuse and the length of one leg of one right triangle must be equal to the hypotenuse and corresponding length of the one leg of the other ∆ for both triangles to be equal by the HL Congruence Theorem.

Thus, let's find x and y by setting the corresponding lengths of the two right ∆s equal to each other.

Therefore:

x = y + 1 › eqn. 1

2x + 3 = 3y + 3 › eqn. 2

Substitute x = (y + 1) into eqn. 2, and solve for y.

2x + 3 = 3y + 3 › eqn. 2

2(y + 1) + 3 = 3y + 3

2y + 2 + 3 = 3y + 3

2y + 5 = 3y + 3

Collect like terms

2y - 3y = -5 + 3

-y = -2

Divide both sides by -1

y = 2

Substitute y = 2 into eqn. 1.

x = y + 1 › eqn. 1

x = 2 + 1

x = 3

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)