Question

Line c ¢ d bisects a ¢ b — at point g. If ae = be, which equation must be true?

1) ae = eg
2) be = eg
3) ae = bg
4) be = bg

Answer 1

Given AE = BE and line c bisects line a at point G, the equation that must be true is AE = BG, which means AG = GB since G is the midpoint of AB.

Step-by-step explanation:

The question involves understanding the properties of a line that bisects another line and applying this knowledge to find which equation must be true given that AE = BE and line c bisects a at point G. Since line c bisects line a at point G, it means that point G is the midpoint of line a. Therefore, the two segments on each side of G (AG and GB) must be equal. Given AE = BE and G bisects the line segment AB, it is clear that AG = GB since G is the midpoint. Since AE = AG + GE and BE = GB + GE, and knowing that AE = BE, we can infer that AG = GB, which means AE = BG or BE = AG. Therefore, the equation that must be true is option 3, AE = BG because AE is equal to AG, and G is the midpoint making AG and BG equal.