Question

Select the correct answer from each drop-down menu. Given: Prove that three lines AD, CF, and BE are intersecting each other at the midpoint O. Complete the proof. It is given that ______ and ______. By ______, ______. Therefore, ______. By ______, ______, and by ______, ______. After the application of ______, ______.

1) AD = CF, BE
2) AD = BE, CF
3) CF = BE, AD
4) BE = AD, CF

Answer 1

To prove that the three lines AD, CF, and BE intersect each other at the midpoint O, we can use the given information and apply relevant geometric principles. By applying the definition of midpoint and transitive property of congruence, we can establish that O is the midpoint of both AD and CF.

Step-by-step explanation:

To prove that the three lines AD, CF, and BE intersect each other at the midpoint O, we can use the given information and apply relevant geometric principles.

Given: AD = CF and it is also given that BE intersect AD at point O.

By the definition of midpoint, we know that if a point O is the midpoint of a line segment EF, then EO = OF. Since BE intersects AD at point O, we can conclude that BO = OD. Similarly, since AD = CF, the line segment AO is congruent to CO. Therefore, by the definition of midpoint, we can conclude that O is the midpoint of the line segment CF.

By the transitive property of congruence, if AO is congruent to CO and BO = OD, then BO is congruent to OD. Hence, by the definition of midpoint, we can conclude that O is the midpoint of the line segment AD as well.

After the application of the given information and the relevant geometric principles, we can prove that three lines AD, CF, and BE intersect each other at the midpoint O. Hence, the correct answer is option 4) BE = AD, CF.