The figure below shows a quadrilateral ABCD Sides AB and DC

The figure below shows a quadrilateral ABCD. Sides AB and DC are equal and parallel: A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram: Side AB is parallel to side DC so the alternate interior angles angle ABD and angle CDB, are congruent. Side AB is equal to side DC and DB is the side common triangles ABD and CDB. Therefore, the triangles ABD and CDB are congruent by SAS postulate. By CPCTC, angles DBC and BDA are congruent and sides AD and BC are congruent. Angle DBC and angle BDA form a pair of vertical angles which are congruent. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is m because its opposite sides are equal and parallel. Which statement best describes a flaw in the student\'s proof? Triangles ABD and BCD are congruent by the SSS postulate. Triangles ABD and BCD are congruent by the AAS postulate. Angle DBC and angle ADB form a pair of corresponding angles which are congruent. Angle DBC and angle ADB form a pair of alternate interior angles which are congruent.

Solution

The first statement describes flaw in the students proof because

the first statement tells that triangles ABD and BCD are congruent by the SSS congruent, but since the diagnols are not equal in parallelogram therefore the two triangles are not congruent by SSS congruent.