Clara writes the following proof for the theorem, ñif the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.î
claraís proof
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 sas postulate.
4. similarly, triangles aod and boc are congruent.
5. by transitive property, angle abd is equal to angle bdc and angle adb is equal to angle dbc.
6. as the alternate interior angles are congruent the opposite sides of quadrilateral abcd are parallel.
7. therefore, abcd is a parallelogram.
which is the first incorrect statement in clara’s proof?
answer
statement 4
statement 5
statement 6
statement 7