Question

Find the values of X and Y that make these triangles congruent by the HL Theorem

1. X=2, Y=1
2. X=3, Y=2
3. X=6, Y=3
4. X=3, Y=6

Answer 1

(1) x=2y
(2) x+4=3y+1

We have a system of 2 equations and 2 unkwons. Using the method of substitution: Replacing the first equation x=2y in the second equation:
(2) 2y+4=3y+1
Solving for y:
2y+4-2y-1=3y+1-2y-1
3=y
y=3

Replacing y=3 in the first equation:
(1) x=2y
x=2(3)
x=6

Answer: Option 3. x=6, y=3