Question 1192419
**1. Definition of Midpoint:**

* Since O is the midpoint of XY, we know that OX ≅ OY.
* Since O is the midpoint of AB, we know that OA ≅ OB.

**2. Vector Addition:**

* Express XA as the sum of vectors: XA = XO + OA 
* Express BY as the sum of vectors: BY = BO + OY

**3. Substitute with Equal Vectors**

* Since OX = -OY and OA = -OB, we can substitute:
    * XA = -OY + OA
    * BY = -OA + OY

**4. Rearrange**

* XA = -OY + OA 
* BY = OY - OA

* Observe that XA and BY are the same vector but with opposite signs.

**5. Conclusion**

* Since XA and BY have the same magnitude but opposite directions, they are congruent.

**Therefore, if two intersecting line segments meet at their midpoints, the line segments joining their endpoints are congruent.**

This proof utilizes vector concepts to demonstrate the congruence of the line segments.