Parallelogram Proofs

Opposite sides of a parallelogram are congruent.

definition of parallelogram

Prove

CPCTC

$$\overline{BR}$$  and  $$\overline{KA}$$  

  $$\overline{AB}$$  and  $$\overline{RK}$$  

 $\overline{BR}$  and  $\overline{RK}$  

  $\overline{AB}$  and  $\overline{KA}$  

Symmetric Property

CPCTC

Reflexive Property

SSS

ASA

SAS

AAS

SSS

Opposite sides of a parallelogram are congruent.

definition of parallelogram

Prove

CPCTC

Opposite sides of a parallelogram are congruent.

definition of parallelogram

Prove

CPCTC

Same-side interior angles theorem

alternate interior angles theorem

consecutive angles theorem

supplementary angles

Definition of a parallelogram

Definition of a quadrilateral

opposite sides are congruent property

opposite sides are supplementary

Alternate interior angles are congruent.

Vertical angles are congruent.

Reflexive Property

$$\parallel\longrightarrow$$ alternate interior angles are congruent

$$\overline{AR}\cong\overline{RA}$$  

$$\overline{AR}\cong\overline{AR}$$  

$$\angle ABR\cong\angle RKA$$  

$$\overline{KA}\cong\overline{AK}$$