Question

if \\( \overline { c d } \cong \overline { d e } \\) and \\( b c = 40 \\), what is \\( b e \\)?

Explanation:

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

Since \(\overline{CD}\cong\overline{DE}\), \(\angle CBD=\angle EBD = 90^{\circ}\), and \(\overline{BD}\cong\overline{BD}\) (common side), then \(\triangle CBD\cong\triangle EBD\) by the HL congruence theorem for right - triangles.

Step2: Use the property of congruent triangles

If \(\triangle CBD\cong\triangle EBD\), then their corresponding sides are equal. That is, \(BC = BE\).

Answer:

\(40\)