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? (1 point)

AAS Postulate

HL Postulate

SAS Postulate

SSS Postulate

The Side Angle Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

AB is congruent to DC, and DB is the side common to triangles ABD and BCD. The included angle between sides AB and DB is angle ABD which is congruent with angle BDC, the angle included between sides DB and DC.

jacobml jacobml · Answer 2 · 2020-11-17T19:32:35+01:00

jacobml jacobml

17-11-2020

Answer:

Its SAS Postulate

Step-by-step explanation: I just got it right on the test, goodluck!

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