Question

for what values of x and y are the triangles to the right congruent by hl? x = and y =

Explanation:

Step1: Apply HL - Hypotenuse - Leg congruence

For right - angled triangles to be congruent by HL, the hypotenuses and one pair of legs must be equal.
Set the hypotenuses equal: $x + 2=3y$.
Set the legs equal: $x=y + 6$.

Step2: Substitute $x$ in the first equation

Substitute $x=y + 6$ into $x + 2=3y$.
$(y + 6)+2=3y$.
Simplify the left - hand side: $y+8 = 3y$.

Step3: Solve for $y$

Subtract $y$ from both sides: $8=3y - y$.
$8 = 2y$.
Divide both sides by 2: $y = 4$.

Step4: Solve for $x$

Substitute $y = 4$ into $x=y + 6$.
$x=4 + 6$.
$x = 10$.

Answer:

$x = 10$ and $y = 4$