Question

question 3 of 10
if \\( \triangle a b c \cong \triangle d b c \\), then \\( b \\) is the midpoint of \\( \overline{a d} \\).
a. true
b. false

Explanation:

Step1: Use the property of congruent triangles

If \(\triangle ABC\cong\triangle DBC\), then \(AB = DB\) (corresponding parts of congruent triangles are equal).

Step2: Recall the definition of a mid - point

A mid - point \(B\) of a line segment \(\overline{AD}\) satisfies \(AB=BD\). Since \(AB = DB\) from the congruence of \(\triangle ABC\) and \(\triangle DBC\), by the definition of a mid - point, \(B\) is the mid - point of \(\overline{AD}\).

Answer:

A. True