Question

in the diagram, ad is the perpendicular bisector of eb. what additional information is needed to prove \\( \triangle abc \cong \triangle dec \\) by hl? enter your answers in the boxes. side \\( \square \cong \\) side \\( \square \\)

Explanation:

Step1: Recall the HL (Hypotenuse - Leg) Congruence Theorem

The HL theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent. In \(\triangle ABC\) and \(\triangle DEC\), \(\angle ACB=\angle DCE = 90^{\circ}\) (since \(AD\) is the perpendicular bisector of \(EB\)). The legs are \(BC\) and \(EC\) (because \(AD\) is the perpendicular bisector of \(EB\), so \(EC = BC\)).

Step2: Identify the hypotenuses

The hypotenuses of \(\triangle ABC\) and \(\triangle DEC\) are \(AB\) and \(DE\) respectively.

Answer:

\(AB\cong DE\)