Question

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?

A. AAS Postulate

B. HL Postulate

C. SAS Postulate

D. SSS Postulate

Answer 1

SAS :)

Explanation:

My test actually has this question, but a different part is missing, so I have the proof for your question :D

Here's mine:

Side AB is equal to side DC, and DB is the side common to triangles ABD and CDB. Angle ABD is congruent to angle CDB by Alternate Interior Angles. Therefore, the triangles ABD and CDB 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 ___<form a pair of alternate interior angles>_____. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

The sentence "Therefore, the triangles ABD and CDB are congruent by SAS postulate" gives you your answer. Hope this helped!

Answer 2

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Answer:

C. SAS Postulate

Explanation:

The student has shown two sides and the angle between them to be congruent. The appropriate postulate is the one whose name reflects that:

Side-Angle-Side postulate (SAS, for short)