Question

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel: A quadrilateral ABCD is shown with the opposite sides AB and DC shown parallel and equal 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 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 _______________. 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 phrase best completes the student's proof? AAS Postulate HL Postulate SAS Postulate SSS Postulate

Answer 1

A Quadrilateral A B C D in which Sides AB and DC are congruent and parallel.

The student has written the following explanation

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 SAS.

The student has also written

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.

Postulate SAS completely describes the student's proof.

Because if in a quadrilateral one pair of opposite sides are equal and parallel then it is a parallelogram.