Question

HELPPPP PLZZZZZ

Find the values of x and y that make these triangles congruent by the HL Theoxen.
22 - 1
y-3
y-1
x = -2, y = 3
x = 2, y = 3​

Answer 1

see below

Explanation:

For the HL theorem to be applicable, the hypotenuses must be the same length:

x+3 = y-1

and the marked legs must be the same length:

y-3 = 2x-1

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Recognizing y-3 = (y-1) -2, we can substitute into the second equation using the first equation:

(y -1) -2 = 2x -1

(x +3) -2 = 2x -1 . . . substitute for y-1

2 = x . . . . . . . . . . add 1-x to both sides

Then the first equation tells us ...

x+4 = y = 2+4 = 6

The values of x and y are ...

x = 2, y = 6