Question

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel.
A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram.

Answer 1

Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and BCD are congruent by SSS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.
Which statement best describes a flaw in the student’s proof?
Answer

Triangles ABD and CDB are congruent by the SAS postulate.

Triangles ABD and BCD are congruent by the AAS postulate.

Angle DBC and angle ADB form a pair of vertical angles which are congruent.

Angle DBC and angle ADB form a pair of corresponding angles which are congruent.

Answer 2

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Answer 3

. Side AB is parallel to side DC
. so the alternate interior angles, angle ABD and angle BDC are congruent.
. Side AB is equal to side DC
. and DB is the side common to triangles ABD and BCD.

Therefore, the triangles ABD and CDB are congruent by \(\large SAS\) postulate.
......you have 2 sides AND the angle between them

Answer 4

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