Question

the figure below shows a part of a framework of a structure. the line segments are girders that give the structure support. if \\( \overline{el} = \overline{lh} \\), \\( \overline{ef} = 5 \\) ft, and \\( \overline{lf} = 4.5 \\) ft, what is the length of \\( \overline{hf} \\)?

Explanation:

Step1: Use Hypotenuse - Leg (HL) Congruence Theorem

Since \( \overline{EL}=\overline{LH}\), \( \angle ELF = \angle HL F=90^{\circ}\), and \( \overline{LF}=\overline{LF}\) (common side), by the Hypotenuse - Leg (HL) Congruence Theorem, \( \triangle ELF\cong\triangle HLF\).

Step2: Use the property of congruent triangles

If two triangles \( \triangle ELF\) and \( \triangle HLF\) are congruent, then their corresponding sides are equal. That is, \( \overline{EF}=\overline{HF}\).

Answer:

\(5\) ft