Question

Line CD bisects line segment AB at point G. If AE = BE, which equation must be true?
A. BE = BG
B. AE = 2(BG)
C. AE = BG
D. AG = BG
E. none of these

Answer 1

Given the information, let's analyze the relationship step by step.

1. **Line CD bisects line segment AB at point G**:
- This means that point G is the midpoint of segment AB.
- Thus, \( AG = GB \).

2. **AE = BE**:
- Here, we are given another equality, which states that the distances AE and BE are equal.

To check which equation is true based on the given conditions:
- Since AE = BE, we are given that these two segments are equal, however, AE and BE are not directly related to point G without further information.

From the given options:
A. **BE = BG**: There's no direct information connecting BE with BG without further relationships.
B. **AE = 2(BG)**: This equation suggests that AE is double the length of BG, but we don't have that connection given directly.
C. **AE = BG**: We do not have a direct relationship between AE and BG.
D. **AG = BG**: This is true because G is the midpoint of AB.

Therefore, the correct equation based purely on the given relationships and the midpoint property is:
**D. AG = BG**