Question

which value of x would make △suv ≅ △tuw by hl? 2 3 4 5

Explanation:

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

For right - triangles \(\triangle SUV\) and \(\triangle TUW\), by HL, the hypotenuses must be equal. So, \(SV = TW\).
Given \(SV=2x + 9\) and \(TW = 4x-1\), we set up the equation \(2x + 9=4x-1\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(2x+9-2x=4x - 1-2x\), which simplifies to \(9 = 2x-1\).
Add \(1\) to both sides: \(9 + 1=2x-1 + 1\), so \(10=2x\).
Divide both sides by \(2\): \(\frac{10}{2}=\frac{2x}{2}\), and \(x = 5\).

Answer:

\(5\) (the fourth option)