Answer:
20. AD = DC
21. AM = 9
22. x = 4 , RS = 3
Explanation:
* Lets explain how to solve the problems
20)
- A mid-point is the point which divides a line segment into two equal
parts in lengths
∵ D is the mid-point of AC
∴ D divides segment AC into two equal parts in lengths
∴ AD = DC
21)
- Line l is a segment bisector of AC at point M
∵ Segment l bisects AC at M
∴ M is the mid point of AC
∴ AM = MC
∵ AM = y + 6
∵ MC = 4y - 3
∴ 4y - 3 = y + 6
- Subtract y from both sides
∴ 3y - 3 = 6
- Add 3 to both sides
∴ 3y = 9
- Divide both sides by 3
∴ y = 3
- Substitute the value of y in AM to find its length
∴ AM = 3 + 6 = 9
∴ AM = 9
22)
- Points R, S, T are col-linear and S is between R and T
∴ RT = RS + ST
∵ RS = 2x - 5
∵ ST = 3x + 2
∵ RT = 17
- Substitute these value in the equation above
∴ 2x - 5 + 3x + 2 = 17
- Add like terms in the left hand side
∴ 5x - 3 = 17
- Add 3 to both sides
∴ 5x = 20
- Divide both sides by 5
∴ x = 4
* The value of x is 4
- Substitute the value of x in RS
∴ RS = 2(4) - 5 = 8 - 5 = 3
∴ The length of RS = 3