Proving Parallelogram Properties

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• opposite sides congruent (6.1)

• opposite angles congruent (6.2)

• diagonals are mutual bisectors (6.3)

• Not a parallelogram.

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• opposite sides congruent (6.1)

• opposite angles congruent (6.2)

• one set of sides is parallel and congruent (6.4)

• Not a parallelogram.

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• opposite sides congruent (6.1)

• opposite angles congruent (6.2)

• one set of sides is parallel and congruent (6.4)

• Not a parallelogram.

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• diagonals are mutual bisectors (6.3)

• opposite angles congruent (6.2)

• one set of sides is parallel and congruent (6.4)

• Not a parallelogram.

What is reason #3? Make sure you write-in the reasons on your proofs.

• Definition of a parallelogram

• Definition of a quadrilateral

• opposite sides are congruent property

• opposite sides are supplementary

Fill in the Reason.

• Opposite sides of a parallelogram are congruent.

• definition of parallelogram

• Prove

• CPCTC

Match the missing statements & reasons in the proof.

f

b

d

e

a

c

g

Reflexive

Opp sides Parallel in Parallelogram

CPCTC

Rhombus 4 = sides

ABCD Rhombus

ABCD is Parallelogram

A parallelogram ABCD is shown. Anna is asked to prove that AB≅DC and AD≅BC. Help her complete her proof by using the given statements and reasons under the figure. Fill in the missing steps and reasons in the proof provided.

• AC is a transversal of AD and BC

• 
• Definition of Parallelogram

• 
• Reflexive Property of Congruence

• 
• △ABC≅△CDA

• 
• Congruent Parts of Congruent Triangles

• 

Prove the following theorem by completing the paragraph proof: "If a quadrilateral is a parallelogram, then the opposite sides are congruent. By the ​ ​ (a)   , AB || CD and BC || AD. Let AC be the transversal of AB and DC. So ∠A ≅ ∠C and ∠B ≅ ∠D by the alternate interior angles theorem. AC ≅ AC by the​ (b)   . ΔABC ≅ ΔCDA by ​ (c)   congruence criterion. AB≅CD and BC≅AD by ​ (d)   ."

• congruent parts of congruent triangles

• definition of parallelogram

• Reflexive Property of Congruence

• SAS≅

• SSS≅

• ASA≅

• Congruent Parts of Congruent Triangles

Prove the following theorem by completing the paragraph proof: "If a quadrilateral is a parallelogram, then the opposite sides are congruent.

By the ​ ​ (a)   , AB || CD and BC || AD. Let AC be the transversal of AB and DC. So ∠A ≅ ∠C and ∠B ≅ ∠D by the alternate interior angles theorem. AC ≅ AC by the​ (b)   . ΔABC ≅ ΔCDA by ​ (c)   congruence criterion. AB≅CD and BC≅AD by ​ (d)   ."

• congruent parts of congruent triangles

• definition of parallelogram

• Reflexive Property of Congruence

• SAS≅

• SSS≅

• ASA≅

• Congruent Parts of Congruent Triangles