Question

which of the following in not always true of parallelogram ABCD A) segment AB is congruent to segment DCB) segment BC is congruent to segment AD C) angle A and angle C are supplementary (add to 180) D) AB+BC=AD+DC

Answer 1

We can answer this question as follows:

Case A:

Segment AB is congruent to segment DC. That is always true. The opposite sides of a parallelogram are congruent.

Case B:

Segment BC is congruent to segment AD. That is always true. The opposite sides of a parallelogram are congruent.

Case C:

This is NOT always true. What is true is that consecutive pairs of angles of a parallelogram are supplementary. For example,

Case D:

AB+BC=AD+DC. This is always true. The diagonal that goes from vertex A to vertex C divides the parallelogram into two congruent triangles. Therefore, this statement is always true.

Therefore, the option that is NOT always true is Angle A and angle C are supplementary (add to 180) (option C).