Question

1. the statements of the proof are given. match each statement to the correct reasoning.

given: c is the midpoint of \\( \overline { a d } \\).
\\( 2 x = 12 \\)
\\( c \\) is the midpoint of \\( a d \\)
\\( x = 6 \\)
\\( a c = c d \\)
\\( 4 x = 2 x + 12 \\)
choices
substitution property of equality
division property of equality
given
subtraction property of equality
definition of midpoint

Explanation:

Step1: Analyze \(2x = 12\)

Subtract \(2x\) from \(4x=2x + 12\) (using Subtraction Property of Equality).

Step2: Analyze \(C\) is the midpoint of \(AD\)

This is given in the problem statement (using Given).

Step3: Analyze \(x = 6\)

Divide both sides of \(2x=12\) by \(2\) (using Division Property of Equality).

Step4: Analyze \(AC = CD\)

By the Definition of Midpoint (a mid - point divides a segment into two equal parts).

Step5: Analyze \(4x=2x + 12\)

Since \(C\) is the mid - point (\(AC = CD\)), substitute \(AC = 4x\) and \(CD=2x + 12\) (using Substitution Property of Equality).

Answer:

• \(2x = 12\): Subtraction Property of Equality
• \(C\) is the midpoint of \(AD\): Given
• \(x = 6\): Division Property of Equality
• \(AC = CD\): Definition of Midpoint
• \(4x=2x + 12\): Substitution Property of Equality