Question

triangle congruence: sss and hl
which value of x would make △suv ≅ △tuw by hl?
(options: 3, 4, 2, 5)
(image of triangles suv and tuw with right angles at u, segments vu and uw marked congruent, sv = 2x + 9, tw = 4x - 1)

Explanation:

Step1: Identify HL Congruence Requirement

For right triangles to be congruent by HL (Hypotenuse - Leg), the hypotenuses must be equal. Here, \( SV = TW \), so \( 2x + 9 = 4x - 1 \).

Step2: Solve the Equation

Subtract \( 2x \) from both sides: \( 9 = 2x - 1 \).
Add 1 to both sides: \( 10 = 2x \).
Divide by 2: \( x = 5 \).

Answer:

5