Question

could δjkl be congruent to δxyz? explain.
○ yes, if $overline{jl} cong overline{xz}$.
○ yes, if xz = 10.
○ no, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.
○ no, because the leg of one triangle is equal in length to the leg of the other triangle.
(image shows two right triangles: δjkl (right-angled at j, hypotenuse kl = 10) and δxyz (right-angled at x, leg xy = 10))

Explanation:

To determine if \(\triangle JKL\) and \(\triangle XYZ\) can be congruent, we analyze the right triangles. In \(\triangle JKL\), the side of length 10 is the hypotenuse (opposite the right angle at \(J\)). In \(\triangle XYZ\), the side of length 10 is a leg (adjacent to the right angle at \(X\)). For right triangles to be congruent, corresponding sides (legs and hypotenuse) must match. Here, the hypotenuse of one (\(KL = 10\)) equals a leg of the other (\(XY = 10\)), which violates congruence conditions for right triangles (e.g., HL, SAS, SSS for right triangles require hypotenuse and leg or two legs/hypotenuse to match). So the correct reasoning is that no, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.

Answer:

No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.