Question

Please Help me ): Medal and fan!

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

Answer 1

Terra's proof

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

Which is the first incorrect statement in Terra's proof?

Answer 2

@ganeshie8 @myininaya help me please ):

Answer 3

Well start with the first statement
Is that a true statement?

Answer 4

Yes!

Answer 5

2nd statement?

Answer 6

Yes

Answer 7

Both of those statements are true because we get to suppose there true from the if part of your statement.
It says we get to believe the diagonals of a quadrilateral bisect each other .

Answer 8

so three is incorrect?

Answer 9

why do you think that? :)

Answer 10

because doesn't supplemental mean that they are equal from parallel lines? something like that lol

Answer 11

supplemental angles add up to 180
those angles should be equal in your picture actually

angle 1 + angle 3 =180 (they lie on that same line
so angle 2+ angle 3=180
therefore angle 2=angle 1