Q:

# 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?

Accepted Solution

A:
Answer:The  ΔABD and ΔCDB are congruent by SAS concurrency. Step-by-step explanation:First please take a look with diagram in attachment. In ΔABD and ΔCDBAB=CD                             { Given in question}$$\angle ABD=\angle CDB$$           {Alternate angle AB || CD}BD=DB                              {Common in both triangle}Therefor, ΔABD and ΔCDB are congruent by SAS$$\angle DBC=\angle ADB$$  by CPCTAD=CB  by CPCTBut $$\angle DBC$$ and $$\angle ADB$$ are pair of alternate interior angle. Therefore, AD parallel to CB (AD||CB)  and  AD=CBWe are given AB parallel to CD (AB||CD) and AB=CDIt means quadrilateral ABCD would be parallelogram because opposite sides are equal and parallel.