Question

1. find the values of x and y that make these triangles congruent by the hl theorem.

o x = 5, y = -6
o x = -5, y = 6
o x = 5, y = 6
o x = 6, y = 5

Explanation:

Step1: Apply HL - Hypotenuse - Leg theorem

For right - angled triangles to be congruent by HL theorem, the hypotenuses and one pair of legs are equal. So we set up two equations: $x=y - 1$ and $3x-2=2y + 1$.

Step2: Substitute $x=y - 1$ into $3x-2=2y + 1$

$3(y - 1)-2=2y+1$. Expand the left - hand side: $3y-3 - 2=2y + 1$, which simplifies to $3y-5=2y + 1$.

Step3: Solve for $y$

Subtract $2y$ from both sides: $3y-2y-5=2y-2y + 1$, so $y-5=1$. Then add 5 to both sides: $y=1 + 5=6$.

Step4: Solve for $x$

Since $x=y - 1$ and $y = 6$, then $x=6 - 1=5$.

Answer:

C. $x = 5,y = 6$