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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?

Respuesta :

Blitztiger
The best words to fill in the blank are "the SAS theorem". We are given that AB is congruent to DC, and that angle ABD is congruent to angle BDC. Then the common side of DB for both triangles is obviously equal to itself (reflexive property). Therefore we have two sides and the angle between them that are congruent, so this uses the SAS theorem to prove that the triangles are congruent.

Answer:

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

Step-by-step explanation:

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