CK-12 Geometry-Concepts

http://www.ck12.org Chapter 6. Polygons and Quadrilaterals

are congruent. To use the Parallelogram Diagonals Converse, you would need to use themidpoint formulafor each
diagonal to see if the midpoint is the same for both. Finally, you can use the last Theorem in this Concept (that if one
pair of opposite sides is both congruent and parallel then the quadrilateral is a parallelogram) in the coordinate plane.
To use this theorem, you would need to show that one pair of opposite sides has the same slope (slope formula) and
the same length (distance formula).

Example A

Write a two-column proof.

Given:AB||DCandAB∼=DC

Prove:ABCDis a parallelogram

TABLE6.6:

Statement Reason

1.AB||DCandAB∼=DC Given

2.^6 ABD∼=^6 BDC Alternate Interior Angles
3.DB∼=DB Reflexive PoC
4. 4 ABD∼= 4 CDB SAS
5.AD∼=BC CPCTC
6.ABCDis a parallelogram Opposite Sides Converse

Example B

Is quadrilateralEF GHa parallelogram? How do you know?

For part a, the opposite angles are equal, so by the Opposite Angles Theorem Converse,EF GHis a parallelogram.
In part b, the diagonals do not bisect each other, soEF GHis not a parallelogram.

Example C

Is the quadrilateralABCDa parallelogram?