Line Segment AE contains points B, C, and D. The measures of the segments are as follows: AB = 3, BC = 4, CD = 5, and DE = 6. Line segment AD is cut by a perpendicular bisector.

Question

What is the length of one of the congruent segments formed as a result of the perpendicular bisector?
A.6
B.7
C.8
D.9

Answer 1

To solve the problem, we first need to determine the lengths of the segments involved.

We know the following lengths for the points on line segment AE:

• \( AB = 3 \)
• \( BC = 4 \)
• \( CD = 5 \)
• \( DE = 6 \)

Next, we calculate the total length of segment \( AD \):

1. Finding the length of AD: \[ AD = AB + BC + CD = 3 + 4 + 5 = 12 \]

2. Determining the midpoint of AD: The midpoint of a segment divides it into two equal lengths. The length of \( AD \) is 12 units, so each half (the length of each segment formed by the perpendicular bisector) is: \[ \text{Length of each segment} = \frac{AD}{2} = \frac{12}{2} = 6 \]

Thus, the length of one of the congruent segments formed as a result of the perpendicular bisector is \( 6 \).

The final answer is: A. 6