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Questions and Answers
A trapezoid is a parallelogram.
A trapezoid is a parallelogram.
False
The diagonals of a rectangle bisect each other.
The diagonals of a rectangle bisect each other.
False
An equilateral parallelogram is equiangular.
An equilateral parallelogram is equiangular.
False
The diagonals of a rhombus are equal.
The diagonals of a rhombus are equal.
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There is one right angle in a parallelogram and it is not a rectangle.
There is one right angle in a parallelogram and it is not a rectangle.
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An equiangular rhombus is a square.
An equiangular rhombus is a square.
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The opposite angles of a parallelogram are supplementary.
The opposite angles of a parallelogram are supplementary.
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The diagonals of a rectangle are the bisectors of the angles.
The diagonals of a rectangle are the bisectors of the angles.
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A square is a rectangle.
A square is a rectangle.
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A rhombus is a square.
A rhombus is a square.
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The diagonals of a quadrilateral are perpendicular and the quadrilateral is not a rhombus.
The diagonals of a quadrilateral are perpendicular and the quadrilateral is not a rhombus.
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If a quadrilateral has three angles of equal measure, then the fourth angle must be a right angle.
If a quadrilateral has three angles of equal measure, then the fourth angle must be a right angle.
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The diagonals of an isosceles trapezoid are congruent.
The diagonals of an isosceles trapezoid are congruent.
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The diagonals of a quadrilateral _____ bisect each other.
The diagonals of a quadrilateral _____ bisect each other.
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If the measures of 2 angles of a quadrilateral are equal, then the quadrilateral is _____ a parallelogram.
If the measures of 2 angles of a quadrilateral are equal, then the quadrilateral is _____ a parallelogram.
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If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is _____ a parallelogram.
If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is _____ a parallelogram.
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If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is _____ a parallelogram.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is _____ a parallelogram.
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To prove a quadrilateral is a parallelogram, it is ________ enough to show that one pair of opposite sides is parallel.
To prove a quadrilateral is a parallelogram, it is ________ enough to show that one pair of opposite sides is parallel.
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The diagonals of a rectangle are _____ congruent.
The diagonals of a rectangle are _____ congruent.
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The diagonals of a parallelogram _____ bisect the angles.
The diagonals of a parallelogram _____ bisect the angles.
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A square is _____ a rhombus.
A square is _____ a rhombus.
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The diagonals of a parallelogram _____ bisect the angles of the parallelogram.
The diagonals of a parallelogram _____ bisect the angles of the parallelogram.
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A quadrilateral with one pair of sides congruent and one pair parallel is _____ a parallelogram.
A quadrilateral with one pair of sides congruent and one pair parallel is _____ a parallelogram.
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The diagonals of a rhombus are _____ congruent.
The diagonals of a rhombus are _____ congruent.
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A rectangle _____ has consecutive sides congruent.
A rectangle _____ has consecutive sides congruent.
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A rectangle _____ has perpendicular diagonals.
A rectangle _____ has perpendicular diagonals.
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The diagonals of a rhombus bisect each other.
The diagonals of a rhombus bisect each other.
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The diagonals of a parallelogram are _____ perpendicular bisectors of each other.
The diagonals of a parallelogram are _____ perpendicular bisectors of each other.
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Consecutive angles of a quadrilateral are _____ congruent.
Consecutive angles of a quadrilateral are _____ congruent.
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The diagonals of a rhombus are _____ perpendicular bisectors of each other.
The diagonals of a rhombus are _____ perpendicular bisectors of each other.
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Consecutive angles of a square are _____ complementary.
Consecutive angles of a square are _____ complementary.
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Diagonals of a non-equilateral rectangle are _____ never angle bisectors.
Diagonals of a non-equilateral rectangle are _____ never angle bisectors.
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A rhombus is _____ a square.
A rhombus is _____ a square.
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A rhombus is _____ a rectangle.
A rhombus is _____ a rectangle.
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A quadrilateral with one pair of congruent sides and one pair of parallel sides is _____ a parallelogram.
A quadrilateral with one pair of congruent sides and one pair of parallel sides is _____ a parallelogram.
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Study Notes
Parallelograms and Their Properties
- A trapezoid is never a parallelogram, highlighting the distinction between these two shapes.
- The diagonals of a rectangle always bisect each other, reinforcing the symmetry inherent in rectangular shapes.
- Equilateral parallelograms are sometimes equiangular, meaning that not all equilateral shapes will have equal angles.
- The diagonals of a rhombus are sometimes equal, indicating that equality of diagonals is not a guaranteed property of all rhombi.
- A parallelogram can never have a single right angle without being a rectangle.
Special Cases and Quadrilaterals
- An equiangular rhombus is always a square, as all angles being equal in a rhombus necessitates that all sides are also equal.
- In parallelograms, opposite angles are sometimes supplementary (sum up to 180 degrees).
- Diagonals of a rectangle sometimes serve as angle bisectors but do not always perform this role.
- A square is always classified as a rectangle because it satisfies the properties of rectangles (four right angles).
Characteristics of Other Quadrilaterals
- A kite can never be a square, as they possess different sets of geometric properties.
- The diagonals of a trapezoid are sometimes perpendicular, adding variability among trapezoidal shapes.
- For quadrilaterals, having three angles equal sometimes implies the fourth must be a right angle.
Conditions for Parallelograms
- A quadrilateral with one pair of opposite sides being congruent and parallel is always a parallelogram.
- If both pairs of opposite sides of a quadrilateral are congruent, it is also always a parallelogram.
- To demonstrate a quadrilateral is a parallelogram, it is never sufficient to show just one pair of sides is parallel.
Properties of Diagonals
- The diagonals of a rectangle are always congruent, confirming equal-length diagonals in rectangular formations.
- Diagonals of a parallelogram sometimes bisect the interior angles, depending on its type.
- Diagonals of a rhombus always bisect each other, ensuring that the rhombus retains its symmetrical properties.
- The diagonals of a rhombus are always perpendicular bisectors, reinforcing the unique angles formed at the intersection.
Miscellaneous Properties
- A square is always a rhombus, further establishing the relationship between square and rhombus properties.
- The property of having congruent consecutive angles in a quadrilateral occurs sometimes, depending on the specific shape.
- Diagonals in non-equilateral rectangles are never bisectors of the angles they intersect.
- A rhombus is sometimes a square and sometimes a rectangle, indicating its versatile nature in geometry.
- A quadrilateral with one pair of congruent sides and one pair of parallel sides is sometimes a parallelogram, not enough alone to confirm this classification.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of the properties of parallelograms with this flashcard quiz. Determine whether each statement is true in all cases, some cases, or never. Perfect for geometry students looking to solidify their knowledge.
