Properties and Classifications of Parallelograms

A set of vocabulary flashcards reviewing the geometric properties of parallelograms and the conditions required to classify parallelograms as rectangles, rhombuses, or squares.

Quadrilateral Angle Sum

The geometric rule stating that the sum of the interior angle measures in all quadrilaterals is $360^\circ$.

Parallelogram

A four-sided quadrilateral that contains $2$ sets of parallel sides.

Opposite Sides Property of Parallelograms

The property stating that in any parallelogram, opposite sides are congruent ($\cong$).

Opposite Angles Property of Parallelograms

The property stating that in any parallelogram, opposite angles ($\angle\text{s}$) are congruent ($\cong$).

Consecutive Angles of a Parallelogram

Consecutive pairs of angles in a parallelogram that are supplementary, such that $\angle 1$ is supplementary to $\angle 2$ and $\angle 3$, while $\angle 4$ is supplementary to $\angle 2$ and $\angle 3$.

Same-Side Interior Angles

Angle pairs formed when parallel lines are cut by transversals, demonstrating why consecutive angles in a parallelogram are supplementary.

Diagonals of a Parallelogram Property

The property stating that the diagonals of a parallelogram bisect each other.

Condition for Proving a Parallelogram is a Rectangle

A condition requiring one to show that $1$ angle ($\angle$) is a right angle ($\angle$), given that the quadrilateral is already proven to be a parallelogram.

Conditions for Proving a Parallelogram is a Rhombus

Conditions requiring one to show that consecutive sides are congruent ($\cong$), or to show that $1$ diagonal bisects a pair of opposite angles ($\angle\text{s}$), provided the figure is already known to be a parallelogram.

Condition for Proving a Parallelogram is a Square

A condition requiring one to show $1$ characteristic from the rectangle list and one characteristic from the rhombus list.

Quadrilateral Classification Caution

The requirement that for special conditions (such as right angles or congruent consecutive sides) to be sufficient to prove a figure is a rectangle, rhombus, or square, you must first know that the quadrilateral is a parallelogram.