For what values of x and y are the triangles to the right congruent by hl?

Based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

Recall:

Thus, for both right triangles to be congruent, it means that their hypotenuse and one of their corresponding legs must be equal to each other.

Use this to create two equations and solve to get the value of x and y.

(eqn. 1)

(eqn. 2).

(eqn. 1)

Therefore, based on the Hypotenuse-Length Theorem of Congruence (HL), the values of x and y that will make both right triangles congruent are:

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x = 8 and y = 4

Step-by-step explanation:

For congruency the hypotenuse and a leg must be congruent, that is

3y = x + 4 → (1) ( Equating the hypotenuse )

x = y + 4 → (2) ( equating corresponding legs )

Substitute x = y + 4 into (1)

3y = y + 4 + 4

3y = y + 8 ( subtract y from both sides )

2y = 8 ( divide both sides by 2 )

y = 4

Substitute y = 4 into (2)

x = 4 + 4 = 8