Question

which value of x would make δsuv ≅ δtuw by hl?
○ 2
○ 3
○ 4
○ 5

Explanation:

Step1: Recall HL Congruence

HL (Hypotenuse-Leg) congruence for right triangles: if hypotenuses and one leg are equal, triangles are congruent. Here, \( \triangle SUV \) and \( \triangle TUW \) are right triangles. The legs \( SU = TU \) (marked congruent), so hypotenuses \( SV = TW \).

Step2: Set Up Equation

Given \( SV = 2x + 9 \) and \( TW = 4x - 1 \), set them equal: \( 2x + 9 = 4x - 1 \).

Step3: Solve for x

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

Answer:

\( \boldsymbol{5} \) (corresponding to the option "5")