PLEASE HELP IM FAILING

find the values of x and y that make these triangles congruent by the hl theorem.

A: x = 3, y = 2

B: x=4, y = 8

C:x= 2, y = 3

D: x = –2, y = 3

Option B:

x = 4 and y = 8

Solution:

The two triangles are congruent by HL theorem.

If two triangles are congruent, then the corresponding sides also congruent.

2x - 5 = y - 5

Add 5 on both sides

2x - 5 + 5 = y - 5 + 5

2x = y (1)

Similarly,

y - 3 = x + 1

Add 3 on both sides.

y - 3 + 3 = x + 1 + 3

y = x + 4   (2)

Equate (1) and (2), we get

2x = x + 4

subtract x from both sides.

2x - x = x + 4 - x

x = 4

Substitute x = 4 in (2), we get

y = 4 + 4

y = 8

Therefore x = 4 and y = 8.

Option B is the correct answer.

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