Question

According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD. Construct diagonal A C with a straightedge. It is congruent to itself by the Reflexive Property of Equality. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the same theorem. __________. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.

Answer 1

The parallelogram can be redrawn as,

To Prove: The opposite side of the parallelogram are equal.

Given: In the given parallelogram AB is parallel to CD and BC is parallel to AD.

Construction: Diagonal AC is drawn.

Proof:

`\begin{gathered} AC=AC\text{ (Common)} \\ \angle BAC=\angle DCA\text{ (Alternate angles)} \\ \angle BCA=\angle DAC\text{ (Alternate angles)} \\ \Delta ABC\cong\Delta CDA\text{ (ASA)} \\ AB=CD\text{ (CPCT)} \\ BC=DA\text{ (CPCT)} \end{gathered}`

Thus, traingle ABC is congruent to triangle CDA by ASA congruency theorem is the missing information from the paragraph.