Question

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

Answer 1

x = 6

y = 2

Explanation:

For both triangles to be congruent, their hypotenuse lengths and the corresponding length of the other leg must be equal to each other.

Thus:

x = y + 4 ---› Eqn. 1

x + 2 = 4y ----› Eqn. 2

Substitute x = (y + 4) into equation 2.

(y + 4) + 2 = 4y

y + 4 + 2 = 4y

y + 6 = 4y

y - 4y = -6

-3y = -6

y = 2

Substitute y = 2 into equation 1

x = y + 4 ---› eqn. 1

x = 2 + 4

x = 6