Question

9. Find the values of x and y that make these triangles congruent by the HL Theorem.

Answer 1

x=2 and y=6

Explanation:

By HL Theorem, the hypotenuses of both triangles are congruent to each other in length as well as both legs. Therefore, we create a system of equations to solve for the values of x and y:

2x-1 = y-3

x+3 = y-1

2x-1 = y-3

2x+2 = y

x+3 = (2x+2)-1

x+3 = 2x+2-1

x+3 = 2x+1

x = 2x-2

-x = -2

x = 2

(2)+3 = y-1

5 = y-1

6 = y

Therefore, x=2 and y=6.