Determining If the Figure Is a Parallelogram

Show that GHIJ is a parallelogram. Solve for x.

• x = 2

• x = 5

• x = 8

• x = 1

Show that GHIJ is a parallelogram. Solve for y.

• y = 5

• y = 4

• y = 1

• y = 8

• No. Only one set of angles and sides are given as congruent. The conditions for a parallelogram are not met.
  

• Yes. Opposite angles are congruent to each other. This is sufficient evidence to prove that the quadrilateral is a parallelogram.
  

• Yes. Opposite sides are congruent to each other. This is sufficient evidence to prove that the quadrilateral is a parallelogram.
  

• Yes. One set of opposite sides are congruent, and one set of opposite angles are congruent. This is sufficient evidence to prove that the quadrilateral is a parallelogram.
  

• The angles always stay the same, so ABCD is a parallelogram.
  

• All sides are congruent, so ABCD is a parallelogram
  

• One pair of opposite sides is congruent and parallel, so ABCD is a parallelogram.
  

• One pair of opposite sides is congruent, so ABCD is a parallelogram.
  

The first part of a proof is shown. What is a valid for Step 2?

• Definition of parallelogram.

• When parallel lines are cut by a transversal, alternate interior angles are congruent.

• When parallel lines are cut by a transversal, corresponding angles are congruent.

• Corresponding parts of congruent triangles are congruent.

• SSS

• ASA

• AAS

• SAS

• Vertical angles are congruent
  

• Given

• If a quadrilateral is a parallelogram, opposite angles are congruent.
  

• If both pairs of opposite angles are congruent, a quadrilateral is a parallelogram.
  

• SSS congruence criterion
  

• Vertical angles are congruent
  

• Given

• If a quadrilateral is a parallelogram, opposite angles are congruent
  

• If both pairs of opposite angles are congruent, a quadrilateral is a parallelogram
  

• SSS congruence criterion
  

• SSS congruence criterion
  

• SAS congruence criterion
  

• Corresponding parts of congruent triangles are congruent
  

• If both pairs of opposite sides are congruent, a quadrilateral is a parallelogram
  

• Vertical angles are congruent