Question

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

Answer 1

A student wrote the following sentences to prove that the two pairs of parallel opposite sides of parallelogram ABCD are congruent.

For triangles ABD and CDB, alternate interior angles ABD and CDB are congruent because AB and DC are parallel lines. Alternate interior angles ADB and CBD are congruent because AD and BC are parallel lines. DB is congruent to DB by transitive property. The triangles ABD and CDB are congruent by ASA postulate. As corresponding parts of congruent triangles are congruent, AB is congruent to DC and AD is congruent to BC by CPCTC.
Which statement best describes a flaw in the student’s proof?

Angles ADB and CBD are congruent because they are corresponding angles.

Angles ADB and CBD are congruent because they are vertical angles.

DB is congruent to DB by reflexive property.

DB is congruent to DB by associative property.

Answer 2

@ganeshie8

Answer 3

@amistre64 can you please help me?

Answer 4

by order of elimination, statement 2 is not true and statement 4 is not true

Answer 5

Angles ADB and CBD are NOT vertical angles

Answer 6

DB is congruent to DB because of Reflexive Property

Answer 7

so it is C?

Answer 8

right