High School

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The figure below shows a parallelogram ABCD. Side AB is parallel to side DC, and side AD is parallel to side BC.

A quadrilateral ABCD is shown with the two pairs of opposite sides AD and BC and AB and DC marked parallel. The diagonals are labeled BD and AC.

A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal:

"For triangles ABD and CDB, alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines. Similarly, alternate interior angle ADB is equal to angle CBD because AD and BC are parallel lines. DB is equal to DB by the reflexive property. Therefore, triangles ABD and CDB are congruent by the SAS postulate. Therefore, AB is congruent to DC and AD is congruent to BC by CPCTC."

Which statement best describes a flaw in the student's proof?

A. Angle ABD is congruent to angle CBD because they are vertical angles, not alternate interior angles.
B. Angle ABD is congruent to angle CBD because they are corresponding angles, not alternate interior angles.
C. Triangles ABD and CDB are congruent by the SSS postulate instead of the SAS postulate.
D. Triangles ABD and CDB are congruent by the ASA postulate instead of the SAS postulate.

Answer :

The statement best describes a flaw in the student's proof is:

Option D: Triangles ABD and CDB are congruent to each other by the ASA postulate instead of the SAS postulate

What are the congruent triangles?

There are different congruency theorems such as:

SSS

SAS

ASA

AAS

HL

Now, the ASA theorem states that two triangles that have a pair of corresponding included congruent sides and two pairs of corresponding congruent angles are congruent triangles.

Based on the ASA theorem, triangles ABD and CDB are congruent to each other.

Therefore, the use of SAS theorem by the student is wrong.

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Rewritten by : Jeany

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