Question

find the measure of each segment.
#1) ab

Explanation:

Step1: Identify triangle properties

From the diagram, \( BD \perp AC \) (right angle at \( D \)) and \( AD = DC \) (marked congruent segments), so \( BD \) is the perpendicular bisector of \( AC \). Thus, \( \triangle ABC \) is isosceles with \( AB = BC \).

Step2: Determine length of \( AB \)

Given \( BC = 5 \), by the property of isosceles triangles (perpendicular bisector implies equal sides), \( AB = BC \). So \( AB = 5 \).

Answer:

\( 5 \)