Elba writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:

Elba's proof

1. For triangles AOB and COD, angle 1 is equal to angle 2 as they are vertical angles.
2. AO = OC and BO = OD because it is given that diagonals bisect each other.
3. Therefore, the triangles AOB and COD are congruent by SAS postulate.
4. Similarly, triangles AOD and COB are congruent.
5. By CPCTC, angle ABD is equal to angle CDB and angle ADB is equal to angle CBD.
6. As the _______________ are congruent, the opposite sides of quadrilateral ABCD are parallel.
7. Therefore, ABCD is a parallelogram.

Which is the missing phrase in Elba's proof?

Question

Elba writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:

Elba's proof

1. For triangles AOB and COD, angle 1 is equal to angle 2 as they are vertical angles. 
2. AO = OC and BO = OD because it is given that diagonals bisect each other. 
3. Therefore, the triangles AOB and COD are congruent by SAS postulate. 
4. Similarly, triangles AOD and COB are congruent. 
5. By CPCTC, angle ABD is equal to angle CDB and angle ADB is equal to angle CBD. 
6. As the _______________ are congruent, the opposite sides of quadrilateral ABCD are parallel. 
7. Therefore, ABCD is a parallelogram.

Which is the missing phrase in Elba's proof?

Bearclaws72 · Answer

attachment

Bearclaws72 · Answer

Which is the missing phrase in Elba's proof?

alternate interior angles
 corresponding angles
 corresponding sides
 opposite sides

Bearclaws72 · Answer

@Angle

Bearclaws72 · Answer

Im doing every other question so you should only be doing five @Angle Senpai XD

Angle · Answer

I don't mind checking all of them as long as you put in some effort to learn as we go

Bearclaws72 · Answer

Uhhhhhh sure 
Dammit Im gonna choke XD Ill try and put an effort

Bearclaws72 · Answer

On this one I actually wanted to say Reflexive property >.>

Angle · Answer

in step 5
"angle ADB is equal to angle CBD"
what are these angles called?

Bearclaws72 · Answer

Is it Transversals?

Bearclaws72 · Answer

Wait no

Bearclaws72 · Answer

I hate vocab

Angle · Answer

yeah, it has to do with transversals

Bearclaws72 · Answer

So it is transversals?

Angle · Answer

I'm asking what those angles (I drew) are called http://www.mathsisfun.com/geometry/parallel-lines.html

Bearclaws72 · Answer

Line segments -_-

Angle · Answer

What are these ANGLES called
<img src="https://image.prntscr.com/image/ltYbXoWtQ8SKGWqop-hByw.png" alt="ltYbXoWtQ8SKGWqop-hByw.png" class="bbcode_img" />

Bearclaws72 · Answer

Alternate interior

Angle · Answer

AWESOME

now what are these ANGLES called?
<img src="https://image.prntscr.com/image/RwmSf-B8SL2NjgVnx5O4zQ.png" alt="RwmSf-B8SL2NjgVnx5O4zQ.png" class="bbcode_img" />

Bearclaws72 · Answer

Dammit. Alternate interior again?

Angle · Answer

yup
so there's your answer

"angle ADB is equal to angle CBD"

means that angles ADB and angle CBD are alternate interior angles.

Once you are able to say "that line is a transversal" => you can say "those two lines are parallel"

Bearclaws72 · Answer

Hell yah alright next question XD

1 attachment