Question

The figure below shows a quadrilateral ABCD. Sides AB and DC are equal 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 CDB, 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 BCD are congruent by SAS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB _______________. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which phrase best completes the student's proof? are congruent by the AAS postulate are congruent by the ASA postulate form a pair of alternate interior angles which are congruent form a pair of vertical angles which are congruent

Answer 1

The phrase that best completes the student's proof (that quadrilateral ABCD is a parallelogram)? Angle DBC and angle ADB form a pair of alternate interior angles which are congruent. The answer is C.

Answer 2

To prove ABCD is a parallelogram, the phrase that completes the proof is "Angle DBC and angle ADB form a pair of alternate interior angles which are congruent"

Explanation:

In a parallelogram, opposite sides are equal and parallel.

AB || DC and AB=DC as given. We only need to show AD || BC and AD=BC So, by congruency properties AD=BC is shown. And for showing AD || BC pair of alternate interior angles should be equal.

Hence, Phrase C : 'Angle DBC and angle ADB form a pair of alternate interior angles which are congruent' completes the proof.