Question

for what values of x and y are the triangles to the right congruent by hl? x x + 1 3y y + 7 x = and y =

Explanation:

Step1: Apply HL - Hypotenuse - Leg theorem

For right - angled triangles to be congruent by HL, the hypotenuses and one pair of legs must be equal.
Set the hypotenuses equal: $x + 1=3y$.
Set the legs equal: $x=y + 7$.

Step2: Substitute $x$ in the first equation

Substitute $x=y + 7$ into $x + 1=3y$.
$(y + 7)+1=3y$.

Step3: Simplify the equation

$y+8 = 3y$.
Subtract $y$ from both sides: $8=3y - y$.
$8 = 2y$.

Step4: Solve for $y$

Divide both sides by 2: $y=\frac{8}{2}=4$.

Step5: Solve for $x$

Substitute $y = 4$ into $x=y + 7$.
$x=4 + 7=11$.

Answer:

$x = 11$ and $y = 4$