Question

Important!

For what values of x and y are the triangles congruent?

Answer 1

Answers:
x = 7
y = 4

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Step-by-step explanation:

Focus on the hypotenuse of each triangle. If the triangles are congruent, then surely the corresponding hypotenuses are congruent as well

This means,
BC = ED
6y-8 = 2y+8
6y-2y = 8+8
4y = 16
y = 16/4
y = 4

If y = 4, then
AC = 5x-5y = 5x-5*4 = 5x-20
and
EF = 2y+7 = 2*4+7 = 8+7 = 15

Similar to how the hypotenuses are congruent, the two bottom legs are corresponding and congruent as well.
AC = EF
5x-20 = 15
5x = 15+20
5x = 35
x = 35/5
x = 7

Answer 2

If these are similar triangles, then all sides are proportional to the other triangle.

label it h/a = h/a

h = hypotenuse
a = adjacent leg

6y-8/5x-5y = 2y+8/2y+7

6y-8 * 2y+7 = 2y+8 * 5x-5y
12y^2 + 26y - 56 = 10xy + 40x - 10y^2 - 40y
22y^2 + 66y - 10xy - 40x -56 = 0

solve for the values of x and y
x = 7
y = 4