Question

in the diagram, bc ≅ ef and ∠a and ∠d are right angles. for the triangles to be congruent by hl, what must be the value of x? 8 9 17 34

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

For right - triangles to be congruent by HL, the hypotenuses must be equal. Given \(BC = EF\), and in right - triangles \(ABC\) and \(DEF\) with right - angles at \(A\) and \(D\) respectively, we set up an equation based on the equality of the hypotenuses.

Step2: Set up the equation

We know that \(34=4x + 2\).

Step3: Solve the equation for \(x\)

Subtract 2 from both sides: \(34−2=4x+2 - 2\), which simplifies to \(32 = 4x\). Then divide both sides by 4: \(\frac{32}{4}=\frac{4x}{4}\), so \(x = 8\).

Answer:

8