Exploring Congruence in Parallelograms

What is required to consider a diagonal as a transversal in a parallelogram?

• It must bisect the opposite angles.

• It must be perpendicular to the base.

• It must intersect at least one pair of parallel sides.

• It must divide the parallelogram into two equal areas.

Which angles are congruent due to the transversal intersecting parallel lines in a parallelogram?

• Angle ABD and angle BDC

• Angle DAC and angle DBC

• Angle ABC and angle CDA

• Angle BAD and angle BCD

What theorem is used to prove the congruency of triangles ADB and CBD?

• Side-Angle-Side

• Angle-Side-Angle

• Side-Side-Side

• Angle-Angle-Side

What does congruency of triangles imply about their corresponding sides?

• They intersect at right angles.

• They are perpendicular.

• They are parallel.

• They are of equal length.

How can the equality of opposite sides help in proving a quadrilateral is a parallelogram?

• By proving the sides are parallel.

• By proving the diagonals bisect each other.

• By proving the angles are supplementary.

• By proving the sides are congruent.

What congruency condition is used to prove two triangles within a quadrilateral are congruent by their sides?

• Angle-Angle-Side

• Side-Angle-Side

• Angle-Side-Angle

• Side-Side-Side

What does the congruency of angle ABC and angle DCB indicate about lines AB and CD?

• They are congruent.

• They are parallel.

• They are perpendicular.

• They intersect at a point.

What geometric property is confirmed by congruent alternate interior angles?

• The lines are of equal length.

• The lines intersect at right angles.

• The lines are parallel.

• The lines are perpendicular.

What is the significance of an 'if and only if' statement in the context of parallelograms?

• It implies an unproven theory.

• It indicates a conditional relationship.

• It confirms a bidirectional condition.

• It suggests a possible correlation.

Which statement is true for the sides of a quadrilateral to ensure it is a parallelogram?

• Opposite sides are congruent if they are not parallel.

• Opposite sides are parallel if they are not congruent.

• Opposite sides are congruent if and only if they are parallel.

• Opposite sides are neither congruent nor parallel.