Question

question 15 of 50
the value of ad is:
triangle diagram with a, b, c, d; ad labeled x, dc labeled 32, right angle at b, and segments ab and bc marked as equal
options: 16, 28, 32

Explanation:

Step1: Identify the triangle property

The diagram shows a perpendicular bisector (since \( DB \perp AC \) and \( B \) is the midpoint of \( AC \), as indicated by the tick marks). By the Perpendicular Bisector Theorem, any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. So, \( D \) is on the perpendicular bisector of \( AC \), which means \( AD = CD \).

Step2: Determine the value of \( AD \)

We are given that \( CD = 32 \). From the Perpendicular Bisector Theorem, \( AD = CD \). So, \( AD = 32 \).

Answer:

32