Question

question 10 of 10
based only on the given information, it is guaranteed that \\( \overline { a b } \perp \overline { c d } \\).
given: \\( \triangle a b c \\)
\\( \overline { a d } \cong \overline { b d } \\)
a. true
b. false

Explanation:

Step1: Analyze the given information

We are given that \(AD\cong BD\) in \(\triangle ABC\). But for \(CD\perp AB\) (i.e., \(\overline{AB}\perp\overline{CD}\)), we would need more information such as \(AC = BC\) (so that \(CD\) is the perpendicular bisector by the property of isosceles triangles: in an isosceles triangle, the median from the vertex to the base is also the altitude). Just knowing \(AD = BD\) (a median) is not sufficient to conclude that \(CD\) is perpendicular to \(AB\).

Answer:

B. False