Ac= cb (given)

now,
ac+ ac= ab (ac=ab)
2ac = ab
therefore,
ac= ab/2
ac= 1/2 ab
hence proved

Given:
- A point C lies between points A and B.
- AC = By

To prove:
- AC = 1/2 AB

Proof:
1. Construction:
- Draw a line segment AB.
- Mark a point C on the line segment AB such that AC = By.

2. Statement:
- AC = By

3. Proof:
- Let's assume that AB = x (Length of line segment AB).

4. Statement:
- AC = By

5. Proof:
- Since AC = By and AB = x, we can write the equation as:
AC = AB - BC

6. Statement:
- AC = AB - BC

7. Proof:
- Substituting the values, we get:
By = x - BC

8. Statement:
- By = x - BC

9. Proof:
- Since AC = By, we can write the equation as:
By = x - BC

10. Statement:
- By = x - BC

11. Proof:
- Rearranging the equation, we get:
BC = x - By

12. Statement:
- BC = x - By

13. Proof:
- Since AC = AB - BC, we can write the equation as:
AC = AB - (x - By)

14. Statement:
- AC = AB - (x - By)

15. Proof:
- Simplifying the equation, we get:
AC = AB - x + By

16. Statement:
- AC = AB - x + By

17. Proof:
- Since AC = By, we can write the equation as:
AC = AB - x + AC

18. Statement:
- AC = AB - x + AC

19. Proof:
- Simplifying the equation, we get:
AC = AB - x + AC

20. Statement:
- AC = AB - x + AC

21. Proof:
- Rearranging the equation, we get:
x = 2AC - AB

22. Statement:
- x = 2AC - AB

23. Proof:
- Substituting the values, we get:
x = 2By - By = By

24. Statement:
- x = By

25. Proof:
- Since AB = x, we can write the equation as:
AB = By

26. Statement:
- AB = By

27. Proof:
- Since AC = By and AB = By, we can write the equation as:
AC = AB

28. Statement:
- AC = AB

29. Proof:
- Since AC = AB, we can write the equation as:
AC = 1/2 AB

30. Statement:
- AC = 1/2 AB

31. Proof: