Parallelograms and Geometric Proof

Which is the correct reason for statement 2 in the proof?

• Given

• Transitive Property

• Definition of Congruent Angles

• Vertical Angles are congruent.

What is the missing statement in the proof?

• 2m∠ABD=m∠ABD+m∠ABD

• m∠ABD=m∠DBC

• m∠ABC=m∠ABC

• m∠ABD+m∠ABD=m∠ABD+m∠DBC

What is the justification?

• Symmetric Prop.

• Angle addition postulate

• Reflexive Prop

• Transitive Prop.

In the given proof, what is the statement for step 4?

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

In the given proof, what is the reason for step 2?

• Alternate Exterior Angle are Congruent

• Reflexive Property of Congruence

• Angles that form a linear pair are supplementary.

• Alternate Interior Angles are Congruent.

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

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.

• Congruent Parts of Congruent Triangles

• 
• △ABC≅△CDA

• 
• AC is a transversal of AD and BC

• 
• Reflexive Property of Congruence

• 
• Definition of Parallelogram

• 

In the given proof, what is the reason for final step?

• Reflexive Property of Congruence

• Corresponding Parts of Congruent Triangles are Congruent

• Angles that form a linear pair are supplementary.

• Alternate Interior Angles are Congruent.

Fill in the Reason.

• Opposite sides of a parallelogram are congruent.

• definition of parallelogram

• Prove

• CPCTC