I hope they came out good now. TWO COLUMN PROOF

[Guest]

Hi everybody!
Well now I have these kind of problems about the two column proofs. What I need this time is for you people to check them to see if I did the right steps or if I am missing something. Please help me as much as you can. Thanks in ADVANCE.

HERE ARE THE PROBLEMS!
C
#1 *
/ \
/ \
/ \
/ \
/ 1 2 \
A /__________________\ B
\ /
\ 3 4 /
\ /
\ /
\ /
\ /
*
D

1. Given: ACBD is a square

Prove: Triangle ACB is congruent to triangle ADB

THESE ARE THE ANSWERS THAT I CAME OUT WITH BUT I DON'T KNOW IF THEY ARE RIGHT OR IN THE RIGHT ORDER OR IF I MISSING SOME STEPS.
Statements Reasons

1. ACBD is a square 1. Given

2. < C and < D are right angles. 2. Definition of a square.

3. < 2 is congruent to < 3 & 3. Alt. Interior <‘s are congruent
< 1 is congruent to < 4

4. AB is congruent to AB 4. Congruence of congruent segments

5. Triangle ACB is congruent 5. ASA
To triangle ADB.
____________________________________________________________________

#2 C
*
* l *
* 1 l 2 *
* l *
* l *
*______3_l_4______*
A X B



2. Given: Angle 3 and Angle 4 are right angles, AX is congruent to BX

Prove: Triangle AXC is congruent to Triangle BXC

Statements Reasons

1. < 3 and < 4 are rights <‘s 1. Given
AX is congruent to BX

2. < 3 is congruent to < 4 2. Right Angles

3. CX is congruent to CX 3. Reflexive property

4. Triangle AXC is congruent 4. ASA
To triangle BXC
____________________________________________________________________

#3 D C
_______________________
l 5 2 * l
l * 3 l
l * l
l * l
l 4 * l
l _*_1________________6_l
A B

3. Given: AD is perpendicular to DC, CB is perpendicular to AB, AD is parallel to BC.

Prove: Triangle ABC is congruent to Traingle CDA


Statements Reasons

1. AD is perpendicular to DC, 1. Given
CB is perpendicular to AB
AD is parallel to BC

2. < 5 and < 6 are right <‘s 2. Definition of perpendicular segments.

3. < 5 is congruent to < 6 3. Right angles are congruent.

4. < 3 is congruent to < 4 4. Alt. interior <‘s are congruent.

5. CA is congruent to CA 5. Reflexive

6. Triangle ABC is congruent 6. AAS
To triangle CDA

I TRIED TO DRAW THE FIGURES THE BEST I COULD! THANKS AGAIN!

 

[soroban]

Hello, bismarck!

Your proofs are quite good . . . but they can be made simpler . . .

#1. Given: ACBD is a square.
. . Prove: \(\displaystyle \Delta ACB\) is congruent to \(\displaystyle \Delta ADB\)

      A           C
      * - - - - - *
      | \         |
      |   \       |
      |     \     |
      |       \   |
      |         \ |
      * - - - - - * 
     D           B

1. \(\displaystyle AC\,=\,DB,\;CB\,=\,AD\). . . 1. Def. of square.

2. \(\displaystyle AB\,=\,AB\) . . . . . . . . . . . . . .2. Reflexive property

3. \(\displaystyle \Delta ACB\) cong. \(\displaystyle \Delta ADB\) . . . . . . .3. s.s.s.

#2. Given: \(\displaystyle \angle 3\,=\,\angle4\,=\,90^o,\:AX\,=\,BX\)
. . Prove: \(\displaystyle \Delta AXC\) is congruent to \(\displaystyle \Delta BXC\).

                C
                *
              / | \ 
            /   |   \
          /     |     \
        /      3|4      \
      * - - - - + - - - - *
      A         X         B

1. \(\displaystyle AX\,=\,BX,\:\angle3\,=\,\angle4\) . . . 1. Given

2. \(\displaystyle CX\,=\,CX\). . . . . . . . . . . . . . .2. Reflexive property

3. \(\displaystyle \Delta AXC\) cong. \(\displaystyle \Delta BXC\) . . . . . .3. s.a.s.