Question

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

Explanation:

Step1: Apply the HL (Hypotenuse - Leg) congruence theorem

For two right - angled triangles, if the hypotenuse and one leg are equal.
Set up the equations:
The hypotenuse: \(x + 4=3y\)
The leg: \(x=y + 2\)

Step2: Substitute \(x=y + 2\) into \(x + 4=3y\)

Substitute \(x\) in the first equation:
\((y + 2)+4=3y\)
\(y+6 = 3y\)
\(6=3y - y\)
\(2y=6\)
\(y = 3\)

Step3: Find the value of \(x\)

Since \(x=y + 2\) and \(y = 3\), then \(x=3+2=5\)

Answer:

\(x = 5\) and \(y = 3\)