Question

line cd bisects 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

Explanation:

Step1: Recall the definition of a bisector

A bisector of a line segment divides the segment into two equal parts. Since line \(CD\) bisects \(\overline{AB}\) at point \(G\), by the definition of a bisector, \(AG = BG\).

Step2: Analyze other options

• For option A: \(BE = BG\). There is no information (such as right - angle or specific triangle type) to suggest that \(BE = BG\).
• For option B: \(AE = 2(BG)\). There is no geometric relationship (like mid - segment or specific triangle ratio) given to support this.
• For option C: \(AE = BG\). There is no evidence (e.g., congruent triangles) to show \(AE = BG\).

Answer:

D. \(AG = BG\)