Proof Check

[vampirewitchreine]

Okay, so this one was throwing me off for a bit, but I think that I might have this one down. If you would be ever so kind to check this and make sure that my reasonings are good, I would greatly appreciate it.

(Black are from the book, red is the information that I filled in)


Given: segment AE || segment DC, segment AB is congruent to segment DB
Prove: ▲ABE is congruent to ▲DCB

Statement	Reason
1. segment AE || segment DC, segment AB is congruent to segment DB	1. Given
2. angle ABE is congruent to angle DBC	2. Vertical angles are congruent
3. segment EB is congruent to segment BC	3. Definition of midpoint
4. ▲ABE is congruent to ▲DBC	4. SAS

Okay, so my reasonings for #1 and #2 are obvious.
I chose to use that segment EB was congruent to BC by the definition of midpoint in #3 as B would need to be the midpoint of AD to make both smaller segments (AB and DB) congruent to each other.
For #4, You have sides that are congruent to corresponding parts of the other triangle with an angle between the two sides that is also congruent to the corresponding part of another triangle.

 

[soroban]

Hello, vampirewitchreine!

If you would be ever so kind to check this, I would greatly appreciate it.

(Black are from the book, red is the information that I filled in)

View attachment 1561
Given: segment AE || segment DC, segment AB is congruent to segment DB
Prove: ▲ABE is congruent to ▲DCB

Statement	Reason
1. segment AE || segment DC, segment AB is congruent to segment DB	1. Given
2. angle ABE is congruent to angle DBC	2. Vertical angles are congruent
3. segment EB is congruent to segment BC	3. Definition of midpoint
4. ▲ABE is congruent to ▲DBC	4. SAS

Your statement 3 is very shaky.
$\displaystyle B$ is the midpoint of $\displaystyle AD,$
. . but it is not obvious that $\displaystyle B$ is the midpoint of $\displaystyle EC.$

You didn't use the fact that $\displaystyle AE \parallel DC.$

You could have had:

$\displaystyle \begin{array}{|cc|cc|} \hline 3. & \angle A = \angle D & 3. & \text{alt-int angles} \\ \hline 4. & \Delta ABE \cong \Delta DBC & 4. & ASA \\ \hline \end{array}$

 

[pka]

Okay, so this one was throwing me off for a bit, but I think that I might have this one down. If you would be ever so kind to check this and make sure that my reasonings are good, I would greatly appreciate it.

(Black are from the book, red is the information that I filled in)

View attachment 1561
Given: segment AE || segment DC, segment AB is congruent to segment DB
Prove: ▲ABE is congruent to ▲DCB

Statement	Reason
1. segment AE || segment DC, segment AB is congruent to segment DB	1. Given
2. angle ABE is congruent to angle DBC	2. Vertical angles are congruent
3. segment EB is congruent to segment BC	3. Definition of midpoint
4. ▲ABE is congruent to ▲DBC	4. SAS

Okay, so my reasonings for #1 and #2 are obvious.
I chose to use that segment EB was congruent to BC by the definition of midpoint in #3 as B would need to be the midpoint of AD to make both smaller segments (AB and DB) congruent to each other.
For #4, You have sides that are congruent to corresponding parts of the other triangle with an angle between the two sides that is also congruent to the corresponding part of another triangle.

Your #'s 3&4 are wrong.
It is not given that B is the midpoint of EC.
But you can use alternate interior angles to get ASA.

 

[vampirewitchreine]

Hello, vampirewitchreine!


Your statement 3 is very shaky.
$\displaystyle B$ is the midpoint of $\displaystyle AD,$
. . but it is not obvious that $\displaystyle B$ is the midpoint of $\displaystyle EC.$

This was only an assumption that dawned on my as I stared blankly at the proof for 10 minutes

You didn't use the fact that $\displaystyle AE \parallel DC.$

This was in statement one

You could have had:

$\displaystyle \begin{array}{|cc|cc|} \hline 3. & \angle A = \angle D & 3. & \text{alt-int angles} \\ \hline 4. & \Delta ABE \cong \Delta DBC & 4. & ASA \\ \hline \end{array}$

Thank you for the corrections (you too pka). Proof's are not my strong point, which is why I post them a lot.