Triniti E.
asked • 05/31/17Write a two-column proof for the following information. Given: M is the midpoint of CD; CM = 5x – 2; MD = 3x + 2 Prove: x = 2
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3 Answers By Expert Tutors
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.
STATEMENT REASON
- M is midpoint of CD given
- CM = 5x-2 given
- MD = 3x+2 given
- CM = MD definition of midpoint
- 5x-2 = 3x+2 substitution
- 2x = 4 addition property of equality
- x=2 division property of equality
Kemal G. answered • 05/31/17
Tutor
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Patient and Knowledgeable Math and Science Tutor with PhD
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
Philip P.
tutor
We keep colliding today, Kemal. We must like answering the same types of questions. ;-)
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05/31/17
Kemal G.
Greetings Philip! Yes, you have a broad range. Keep up the good work. :) Best, Kemal
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05/31/17
Jennifer M.
there is a 2nd part to this question here it is Write a two-column proof for the following information. Given: M is the midpoint of CD; MD = 3 Prove: CM = 3
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10/04/20
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Jennifer M.
did you ever get the answer to Write a two-column proof for the following information. Given: M is the midpoint of CD; MD = 3 Prove: CM = 310/04/20