Question

Answer please

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 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 CDB are congruent by SSS postulate. By CPCTC, angles DBC and BDA are congruent and sides AD and BC are congruent. Angle DBC and angle BDA 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 statement best describes a flaw in the student's proof?

Question 11 options:

Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.


Triangles ABD and CDB are congruent by the SAS postulate instead of the SSS postulate.


Triangles ABD and BCD are congruent by the AAS postulate instead of the SSS postulate.


Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.

Answer 1

Answer: Answer is B

Step-by-step explanation: Did FLVS test

Answer 2

• B. Triangles ABD and CDB are congruent by the SAS postulate instead of the SSS postulate.

Explanation:

Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.

• Incorrect, since mentioned angles form a pair of alternate interior angles.

Triangles ABD and CDB are congruent by the SAS postulate instead of the SSS postulate.

• Correct, since AB = CD, BD = DB, ∠ABD ≅ ∠CDB

Triangles ABD and BCD are congruent by the AAS postulate instead of the SSS postulate.

• Incorrect, since not enough evidence for AAS

Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.

• Incorrect, since DBC and BDA are not corresponding according to definition of corresponding angles