Write a two-column proof for the following information. Given: M is the midpoint of CD; CM = 5x – 2; MD = 3x + 2 Prove: x = 2

Question

 I really need help on this problem!

Answer 1

If M is the midpoint of line segment CD, then CM = MD, as the midpoint M will divide line segment CD into two equal parts. Consequently, if the length of CM = the length of MD, then 5x - 2 = 3x + 2.

 

If we solve this equation by isolating the variable terms on one side and the constant terms on the other side of the equation, then we get:

 

2x = 4

 

If we divide the coefficient of x, then we get x = 2.

 

I realize this is not a two-column proof, but it does give you the reasoning behind why x must x = 2.

Answer 2

     STATEMENT                 REASON

1. M is midpoint of CD     given
2. CM = 5x-2                  given
3. MD = 3x+2                 given
4. CM = MD                    definition of midpoint
5. 5x-2 = 3x+2               substitution
6. 2x = 4                        addition property of equality
7. x=2                           division property of equality

Answer 3

Hi Triniti,

 

|CM| = |MD|        M is the midpoint of |CD|

5x - 2 = 3x + 2   the lengths of |CM| and |MD| given

 

5x - 2 = 3x + 2

2x = 4

x = 2