CPM Homework Help : INT2 Problem 7-60

What else can you prove about quadrilaterals? Prove that if a pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral must be a parallelogram. For example, for the quadrilateral $ABCD$ at right, given that $\overline{AB} // \overline{CD}$ and $\overline{AB} ≅ \overline{CD}$ , show that $\overline{BC} // \overline{AD}$ . Organize your reasoning in a proof (two-column or flowchart). Then record your theorem in your Theorem Graphic Organizer.

Quadrilateral A, B, C, D. Side A, B and side C, D are marked with two tick marks and one arrow each.

Hint:

If a pair of opposite sides is parallel and congruent then the quadrilateral is a parallelogram.
Use the if part of the statement as the givens, and the then part of the statement as the prove portion in the proof.

Partial Answer:

Statements	Reasons
$\overline{AB}//\overline{CD}$	Given
	Given
$∠BAC ≅ ∠DCA$
	Segment is congruent to itself
$ΔABC ≅ ΔCDA$
$∠BCA ≅ ∠DAC$
	Alt. int. angles $≅→$ parallel
$ABCD$ is a parallelogram