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 criterion

For two right - angled triangles, if the hypotenuse and one leg are equal.
Set up the equations:

$$\begin{cases} x=y + 7\\ x + 2=4y \end{cases}$$

Step2: Substitute \(x=y + 7\) into \(x + 2=4y\)

Substitute \(x\) in the second equation: \((y + 7)+2=4y\)
Simplify: \(y+9 = 4y\)
Subtract \(y\) from both sides: \(9=4y - y\)
So, \(3y=9\), then \(y = 3\)

Step3: Find \(x\)

Substitute \(y = 3\) into \(x=y + 7\), we get \(x=3 + 7=10\)

Answer:

\(x = 10\) and \(y = 3\)