Question

Select the correct answer from each drop-down menu. Given: Prove that three lines BE, AD, and CF are intersected at the midpoint point O. Complete the proof. Suppose that ______. By the vertical angles theorem, ______. By the transitive property, ______. ______, which contradicts the given. Therefore, ______.

1) AB = BC, AD = DC, BE = EC, and ���AOD = ���COD
2) AB = BC, AD = DC, BE = EC, and ���AOC = ���BOD
3) AB = BC, AD = DC, BE = EC, and ���AOC = ���COD
4) AB = BC, AD = DC, BE = EC, and ���AOD = ���BOD

Answer 1

To prove that three lines BE, AD, and CF intersect at the midpoint point O, we can use the following steps: 1) Suppose that AB = BC, AD = DC, BE = EC, and ∠AOC = ∠BOD. 2) By the vertical angles theorem, ∠AOC = ∠COD and ∠AOD = ∠BOD. 3) By the transitive property, ∠AOC = ∠COD and ∠AOD = ∠COD. 4) This implies that ∠AOC = ∠AOD, which contradicts the given information. Therefore, our supposition is incorrect and the lines BE, AD, and CF do not intersect at the midpoint point O.

Step-by-step explanation:

To prove that three lines BE, AD, and CF intersect at the midpoint point O, we can use the following steps:

1. Suppose that AB = BC, AD = DC, BE = EC, and ∠AOC = ∠BOD.
2. By the vertical angles theorem, ∠AOC = ∠COD and ∠AOD = ∠BOD.
3. By the transitive property, ∠AOC = ∠COD and ∠AOD = ∠COD.
4. This implies that ∠AOC = ∠AOD, which contradicts the given information.
5. Therefore, our supposition is incorrect and the lines BE, AD, and CF do not intersect at the midpoint point O.