Podcast
Questions and Answers
Which statement is true about the diagonals of a parallelogram?
Which statement is true about the diagonals of a parallelogram?
What can be concluded if both pairs of opposite sides of a quadrilateral are congruent?
What can be concluded if both pairs of opposite sides of a quadrilateral are congruent?
Which property is unique to parallelograms compared to general quadrilaterals?
Which property is unique to parallelograms compared to general quadrilaterals?
Which of the following figures is NOT a type of parallelogram?
Which of the following figures is NOT a type of parallelogram?
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If the diagonals of a quadrilateral bisect each other, what can be determined about the quadrilateral?
If the diagonals of a quadrilateral bisect each other, what can be determined about the quadrilateral?
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Which statement about the angles in a parallelogram is correct?
Which statement about the angles in a parallelogram is correct?
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What distinguishes a parallelogram from a trapezoid?
What distinguishes a parallelogram from a trapezoid?
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In a parallelogram, if the measure of one angle is $70^{ ext{o}}$, what is the measure of its consecutive angles?
In a parallelogram, if the measure of one angle is $70^{ ext{o}}$, what is the measure of its consecutive angles?
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Study Notes
Definition of a Parallelogram
- A parallelogram is a quadrilateral with opposite sides parallel.
Properties of a Parallelogram
- Opposite sides are congruent (equal in length).
- Opposite angles are congruent (equal in measure).
- Consecutive angles are supplementary (their sum is 180 degrees).
- Diagonals bisect each other.
Diagonals of a Parallelogram
- The diagonals of a parallelogram do not necessarily have equal lengths.
- They divide the parallelogram into two congruent triangles.
Other Important Observations
- The intersection point of the diagonals is the center of symmetry for the parallelogram.
- A rectangle, rhombus, and square are all special types of parallelograms.
Relationship to Other Quadrilaterals
- A parallelogram has more properties than a general quadrilateral.
- In particular, the properties related to parallel sides are unique to parallelograms.
Parallelogram Theorems
- If a quadrilateral is a parallelogram, then its opposite sides are congruent.
- If a quadrilateral is a parallelogram, then its opposite angles are congruent.
- If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
- If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Determining if a Quadrilateral is a Parallelogram
- If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
- If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
- If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.
- If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
- If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
Examples of Parallelograms
- Rectangles
- Rhombuses
- Squares
Key Differences from other quadrilaterals
- Parallelograms are distinguished by their having two pairs of opposite sides that are parallel and congruent. This differentiates them from trapezoids, which have only one pair of parallel sides.
- A parallelogram is a quadrilateral but not all quadrilaterals are parallelograms.
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Description
Explore the defining features and properties of parallelograms in this quiz. Understand the relationships among their sides, angles, and diagonals, as well as how they relate to other quadrilaterals. Test your knowledge on theorems related to parallelograms.
