Thread: Two column proof proving two line segments are congruent

Here's the figure:

Given that line AX is congruent to line DX, and line XB is congruent to line XB:
Prove that line AC is congruent to line BD.

Code:

 

       Statements                                                       Reasons
     1. Line Ax is congruent to Dx                   1. Given
     2. <AXD is congruent to <BXC                          2. Vertical Angles Theorem       
     3. X is the midpoint of line AC                          3. Definition of a Midpoint
        and line BD. 
     4. Line AC is congruent to line BD.                    4. Definition of a Midpoint

This is my try, I really don't think it's correct, so if somebody could help me out that would be cool.

posted by rogereggbert

i believe there is an error in your givens.Is the second given XB =XC If yes the figure is a parralellogram not a rectangle.It has two congruent triangles with the two legs you want to prove equal

bj

Originally Posted by rogereggbert

Here's the figure:

Given that line AX is congruent to line DX, and line XB is congruent to line XB:
Prove that line AC is congruent to line BD.

Code:

 
 
       Statements                                                       Reasons
    1. Line Ax is congruent to Dx                   1. Given
    2. <AXD is congruent to <BXC                          2. Vertical Angles Theorem       
    3. X is the midpoint of line AC                          3. Definition of a Midpoint
       and line BD. 
    4. Line AC is congruent to line BD.                    4. Definition of a Midpoint

This is my try, I really don't think it's correct, so if somebody could help me out that would be cool.

Yeah, there is an error in the Given. But assuming that it's XB is congruent to XC, this is how I would do it.

Statements Reasons
1. AX is congruent to DX 1. Given.
XB is congruent to XC

2. Angles AXC and BXD are congruent. 2. Vertical angles are congruent.

3. Triangles AXC and DXD are congruent. 3. SAS Postulate

4. AC is congruent to BD. 4. Corresp. parts of congruent
angles are congruent.

Hope this helps! =)