Question

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?

Answer 1

The triangles ABD and CDB are congruent by the Side-Angle-Side (SAS) postulate, leading to the conclusion that quadrilateral ABCD is a parallelogram.

Step-by-step explanation:

The triangles ABD and CDB can be proved congruent by the Side-Angle-Side (SAS) postulate. Since side AB is parallel to side DC, the alternate interior angles angle ABD and angle BDC are congruent. With both triangles sharing side DB and having equal sides AB and DC, the two triangles satisfy the conditions of the SAS postulate.

By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) principle, angles DBC and ADB are congruent as well as sides AD and BC. Since angle DBC and angle ADB form a pair of alternate interior angles, this implies that AD is congruent and parallel to BC. This leads to the conclusion that quadrilateral ABCD is a parallelogram, characterized by its opposite sides being equal and parallel.

Answer 2

Therefore, the triangles ABD and BCD are congruent by SAS postulate

Step-by-step explanation:

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