Understanding Parallelograms

What is the primary difference between a property and a proof when discussing parallelograms?

• A property is always true, while a proof is sometimes true.

• A property is a method, while a proof is a characteristic.

• A property is a visual representation, while a proof is a written explanation.

• A property is a characteristic, while a proof is a method to verify it.

Which of the following is NOT a method to prove a quadrilateral is a parallelogram?

• Diagonals are perpendicular.

• One pair of opposite sides is both congruent and parallel.

• Both pairs of opposite sides are congruent.

• Both pairs of opposite sides are parallel.

How does the video suggest you verify the methods of proving a parallelogram?

• By memorizing the methods.

• By ignoring the methods.

• By practicing with different examples.

• By using a calculator.

In the first proof, what is the significance of finding a pair of corresponding angles?

• It proves that the diagonals bisect each other.

• It helps establish that the sides are equal.

• It shows that the angles are supplementary.

• It indicates that the lines are parallel.

What is the role of substitution in the first proof method?

• To replace angles with sides.

• To establish congruence between different sides.

• To replace given information with new data.

• To simplify the diagram.

What is the importance of marking up the diagram in the first proof?

• To make the diagram look more complex.

• To visually represent the given information and relationships.

• To add unnecessary details.

• To confuse the viewer.

In the second proof, what property of the larger parallelogram is used to help prove the smaller quadrilateral is a parallelogram?

• The opposite sides are parallel.

• The diagonals bisect each other.

• The angles are all right angles.

• The sides are all equal.

Why is subtraction used in the second proof?

• To simplify the proof.

• To establish congruence between smaller segments.

• To find the difference between angles.

• To eliminate unnecessary information.

What is the final step in proving a quadrilateral is a parallelogram in the second proof?

• Demonstrating that all sides are congruent.

• Showing that all angles are equal.

• Establishing one pair of sides is both congruent and parallel.

• Proving the diagonals bisect each other.

Which of the following is a key takeaway from the second proof?

• All quadrilaterals are parallelograms.

• A quadrilateral with one pair of opposite sides congruent and parallel is a parallelogram.

• Only rectangles can be proven as parallelograms.

• Diagonals must be equal for a shape to be a parallelogram.