Answer:
20. AD = DC
21. AM = 9
22. x = 4 , RS = 3
Step-by-step explanation:
* <em>Lets explain how to solve the problems</em>
20)
-<em> A mid-point is the point which divides a line segment into two equal</em>
<em> parts in lengths</em>
∵ D is the mid-point of AC
∴ D divides segment AC into two equal parts in lengths
∴ <em>AD = DC</em>
21)
- <em>Line l is a segment bisector of AC at point M</em>
∵ 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
- <em>Substitute the value of y in AM to find its length</em>
∴ AM = 3 + 6 = 9
∴ <em>AM = 9</em>
22)
<em>- Points R, S, T are col-linear and S is between R and T</em>
∴ RT = RS + ST
∵ RS = 2x - 5
∵ ST = 3x + 2
∵ RT = 17
- <em>Substitute these value in the equation above</em>
∴ 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
* <em>The value of x is 4</em>
- <em>Substitute the value of x in RS</em>
∴ RS = 2(4) - 5 = 8 - 5 = 3
∴<em> </em><em>The length of RS = 3</em>
