Question

using the hl theorem
in the diagram, \\( \overline { b c } \cong \overline { e f } \\) and \\( \angle a \\) and \\( \angle 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 the HL Theorem

For right - angled triangles, if the hypotenuse and one leg are congruent, the triangles are congruent. Here, \(BC\cong EF\) (hypotenuses) and we need \(AB\cong ED\) (legs). Given \(AB = 34\) and \(ED=4x + 2\).

Step2: Set up the equation

Since \(AB\cong ED\), we have the equation \(4x+2=34\).

Step3: Solve the equation

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

Answer:

\(x = 8\), so the answer is \(8\) (the first option).