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

 $\overline{KL}\cong\overline{MN}$  and  $\angle KLM\cong\angle MNK.$  Determine if the quadrilateral must be a parallelogram. Justify your answer.

• 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.
  

A wooden frame has screws at A, B, C, and D so that the sides of it can be pressed to change the angles occurring at each vertex.  $\overline{AB}\cong\overline{CD}$  and  $\overline{AB}\parallel\overline{CD},$  even when the angles change. Why is the frame always 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.

Given  $\overline{AB}\cong\overline{CD}$  and  $\overline{AD}\cong\overline{BC,}$  what triangle congruence criterion is likely to be used in a proof that  $\overline{AB}\parallel\overline{CD}$  and  $\overline{AD}\parallel\overline{BC}?$  

• SSS

• ASA

• AAS

• SAS

 Which of the following is a valid conclusion given parallelogram ABCD with diagonals  $\overline{AC}\ and\ \overline{BD}?$  Identify all of the choices that best complete the statement.

•  $\angle A\cong\angle C$  

•  $\overline{AB}\cong\overline{CD}$  

•  $\overline{AC}\cong\overline{BD}$  

•  $\angle A\ and\ \angle B\$  are supplementary
  

•  $\angle A\cong\angle B$  

 Identify the correct choice that best completes the proof.
 $\overline{AM}\cong\overline{CM};\ \overline{BM}\cong\overline{DM}$  

• 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
  

Identify the correct choice that best completes the proof.
 $\angle AMB\cong\angle CMD;\ \angle AMD\cong\angle CMB$  

• 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
  

Identify the correct choice that best completes the proof.
 $\Delta AMB\cong\Delta CMD;\ \Delta AMD\cong\Delta CMB$  

• 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