Prove Parallelograms

In order to show that a figure is a rhombus, you first need to prove it is a ...

• Quadrilateral

• Square

• Rectangle

• Parallelogram

In order to show that a figure is a rectangle, you first have to prove it is a ....

• Square

• Parallelogram

• Quadrilateral

• Rhombus

In order to show a figure is a square, you need to show it is a ...

• Rhombus

• Rectangle

• Parallelogram

• Parallelogram, Rhombus AND Rectangle

A parallelogram has both pairs of opposite sides ____________.

• Parallel

• Congruent

• Parallel and Congruent

The missing reason is the same for steps 2 and 4. What is the missing reason?

• If alternate interior angles are congruent, then the lines are parallel.

• If vertical angles are congruent, then the lines are parallel.

• Definition of parallelogram

• Alternate interior angles formed by parallel lines are congruent.

Fill in the Reason

• Opposite sides of a parallelogram are congruent.

• definition of parallelogram

• Prove

• CPCTC

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.

• △ABC≅△CDA

• 
• Congruent Parts of Congruent Triangles

• 
• Definition of Parallelogram

• 
• AC is a transversal of AD and BC

• 
• Reflexive Property of Congruence

• 

Choose the correct missing reasons for the proof.

• 4) CPCTC; 6)All quads are parallelograms

• 4) Alternate Interior Angles are congruent; 6) Definition of paralelogram

• 4)CPCTC; 6)Definition of parallelogram

• 4) Alternate Interior Angles are congruent; 6) All quads are parallelograms

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

Fill in the missing reason for the proof.

• If alternate interior angles are congruent, then the lines are parallel.

• Definition of parallelogram

• Definition of parallel lines

• Opposite sides of a parallelogram are congruent.