Question

for what values of x and y are the triangles to the right congruent by hl? x = 8 and y = 3

Explanation:

Step1: Apply the HL (Hypotenuse - Leg) Congruence Theorem

For two right - angled triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of the other triangle, the triangles are congruent.
Set up the equations:
\(x = y + 4\) (legs) and \(x + 2=4y\) (hypotenuses)

Step2: Solve the system of equations

Substitute \(x=y + 4\) into \(x + 2=4y\):
\((y + 4)+2=4y\)
\(y+6 = 4y\)
\(6=4y - y\)
\(3y=6\)
\(y = 2\)

Step3: Find the value of \(x\)

Substitute \(y = 2\) into \(x=y + 4\)
\(x=2 + 4\)
\(x = 6\)

Answer:

\(x = 6\) and \(y = 2\)