Question

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

Melissa'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. The triangles AOB and COD are congruent by SSS postulate.
4. Similarly, triangles AOD and COB are congruent.
5. By CPCTC, AB is equal to DC.
6. By CPCTC, AD is equal to BC.
7. As the opposite sides are congruent the quadrilateral ABCD is a parallelogram.

Answer 1

Which is the first incorrect statement in Melissa's proof?
Statement 5
Statement 3
Statement 4
Statement 6

Answer 2

@Straybullet

Answer 3

I dont know which one it is

Answer 4

It's cool :)
@YanaSidlinskiy, can you help me here?

Answer 5

I think it might be statement 3 thats wrong

Answer 6

Alright, do you think I'd have to make sure?

Answer 7

I''ll open a new one tho :P

Answer 8

1. For triangles AOB and DOC, 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. The triangles AOB and DOC are congruent by SSS postulate...(show that the diagonals bisect each other)
4. Similarly, triangles AOD and BOC are congruent...(show that one pair of opposite sides is both congruent and parallel.)

5. By CPCTC, AB is equal to DC....Corresponding parts of congruent triangles are congruent-doesn't make much sense
6. By CPCTC, AD is equal to BC.
7. As the opposite sides are congruent the quadrilateral ABCD is a parallelogram.
Can you now take a guess?