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 two right - angled triangles to be congruent by HL, the hypotenuse and one leg of one triangle must be equal to the hypotenuse and one leg of the other triangle.
So, we have the following two equations:

1. \(x=y + 3\) (legs are equal)
2. \(x + 1=3y\) (hypotenuses are equal)

Step2: Substitute \(x=y + 3\) into \(x + 1=3y\)

Substitute \(x\) in the second equation:
\((y + 3)+1=3y\)
\(y+4 = 3y\)
\(4=3y - y\)
\(2y=4\)
\(y = 2\)

Step3: Find the value of \(x\)

Substitute \(y = 2\) into \(x=y + 3\)
\(x=2 + 3\)
\(x=5\)

Answer:

\(x = 5\) and \(y = 2\)