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. 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

Answer:

Therefore, the triangles ABD and CDB are congruent by SAS postulate, NOT SSS postulate, which would require 3 pairs of congruent sides.

Answer:2.Triangles ABD and CDB are congruent by the SAS postulate.

Step-by-step explanation:

"Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle CDB, are congruent." is perfectly correct.

"Side AB is equal to side DC and DB is the side common to triangles ABD and BCD." this is also true

so by now we have 2 triangles, with 2 congruent sides, and the angles between these pairs of congruent sides, are also congruent