if the line ab bisects the segment cd at p then p is the mid point of segment cd
looks true to me.
bisecting means dividing into two equal parts.
To prove that point P is the midpoint of segment CD when line AB bisects segment CD at P, you can use the midpoint theorem.
The midpoint theorem states that if a line segment is bisected by another line, then the segment is divided into two equal parts.
Here's how you can prove it:
1. Given that line AB bisects segment CD at point P.
2. Draw line segments AP and BP.
3. Now, you have two triangles formed: triangle ACP and triangle BCP.
4. By the definition of a bisector, line AP is congruent to line BP because they are both radiating from point P.
5. By the reflexive property of congruence, line CP is congruent to line CP.
6. By the side-angle-side (SAS) congruence postulate, triangle ACP is congruent to triangle BCP.
7. By the congruence of corresponding parts of congruent triangles, segment AC is congruent to segment BC.
8. By the definition of congruence, segment AC is equal in length to segment BC.
9. Therefore, point P is the midpoint of segment CD.
By following these steps, you have proven that point P is the midpoint of segment CD when line AB bisects segment CD at P.