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Questions and Answers
Opposite sides of a rectangle are parallel.
Opposite sides of a rectangle are parallel.
Adjacent sides of a rhombus are congruent.
Adjacent sides of a rhombus are congruent.
Diagonals of a rhombus are congruent.
Diagonals of a rhombus are congruent.
Opposite sides of a parallelogram are congruent.
Opposite sides of a parallelogram are congruent.
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Diagonals of a rectangle are perpendicular.
Diagonals of a rectangle are perpendicular.
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Diagonals of a rectangle bisect opposite angles.
Diagonals of a rectangle bisect opposite angles.
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Opposite angles of a parallelogram are congruent.
Opposite angles of a parallelogram are congruent.
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Consecutive angles of a parallelogram are congruent.
Consecutive angles of a parallelogram are congruent.
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Diagonals of a parallelogram bisect each other.
Diagonals of a parallelogram bisect each other.
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The four angles of a rhombus are right angles.
The four angles of a rhombus are right angles.
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Consecutive sides of a rhombus are congruent.
Consecutive sides of a rhombus 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 measure of two angles of a quadrilateral are equal, then the quadrilateral is a parallelogram.
If the measure of two angles of a quadrilateral are equal, 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 that a quadrilateral is a parallelogram, it is sufficient to show that one pair of opposite sides is parallel.
To prove that a quadrilateral is a parallelogram, it is sufficient to show that one pair of opposite sides is parallel.
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If both pairs of opposite angles 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.
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A square is a rhombus.
A square is a rhombus.
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A quadrilateral is a parallelogram.
A quadrilateral is a parallelogram.
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A rectangle is a rhombus.
A rectangle is a rhombus.
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A parallelogram with at least one right angle is a square.
A parallelogram with at least one right angle is a square.
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A trapezoid is a parallelogram.
A trapezoid is a parallelogram.
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A quadrilateral is a trapezoid.
A quadrilateral is a trapezoid.
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The bases of an isosceles trapezoid are congruent.
The bases of an isosceles trapezoid are congruent.
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A parallelogram is a rectangle.
A parallelogram is a rectangle.
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A kite has congruent diagonals.
A kite has congruent diagonals.
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Each diagonal of a parallelogram divides it into two congruent triangles.
Each diagonal of a parallelogram divides it into two congruent triangles.
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A parallelogram whose diagonals are congruent and perpendicular to each other is a square.
A parallelogram whose diagonals are congruent and perpendicular to each other is a square.
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A quadrilateral is a parallelogram if its diagonals are perpendicular.
A quadrilateral is a parallelogram if its diagonals are perpendicular.
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The bases of a trapezoid are congruent.
The bases of a trapezoid are congruent.
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Opposite angles of a parallelogram are supplementary.
Opposite angles of a parallelogram are supplementary.
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If the diagonals of a quadrilateral are perpendicular to each other, the quadrilateral is a square.
If the diagonals of a quadrilateral are perpendicular to each other, the quadrilateral is a square.
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A diagonal of an isosceles trapezoid divides it into two congruent triangles.
A diagonal of an isosceles trapezoid divides it into two congruent triangles.
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A rhombus is equiangular.
A rhombus is equiangular.
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A quadrilateral whose angles are congruent is a rectangle.
A quadrilateral whose angles are congruent is a rectangle.
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If the diagonals of a square are drawn, then the resulting four triangles are isosceles right triangles.
If the diagonals of a square are drawn, then the resulting four triangles are isosceles right triangles.
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If the diagonals of a parallelogram bisect opposite angles, the parallelogram is a square.
If the diagonals of a parallelogram bisect opposite angles, the parallelogram is a square.
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Study Notes
Key Properties of Quadrilaterals
- Opposite sides of a rectangle are always parallel.
- Adjacent sides of a rhombus are always congruent.
- Diagonals of a rhombus are sometimes congruent.
- Opposite sides of a parallelogram are always congruent.
- Diagonals of a rectangle are sometimes perpendicular.
- Diagonals of a rectangle always bisect opposite angles.
- Opposite angles of a parallelogram are sometimes congruent.
- Consecutive angles of a parallelogram are sometimes congruent.
- Diagonals of a parallelogram always bisect each other.
- The four angles of a rhombus are sometimes right angles.
- Consecutive sides of a rhombus are always congruent.
Quadrilaterals and Parallelograms
- Diagonals of a quadrilateral sometimes bisect each other.
- If two angles of a quadrilateral are equal, the quadrilateral is sometimes a parallelogram.
- If both pairs of opposite sides of a quadrilateral are congruent, it is always a parallelogram.
- A sufficient condition to prove a quadrilateral is a parallelogram is never achieved by showing one pair of opposite sides is parallel.
- If both pairs of opposite angles of a quadrilateral are congruent, it is always a parallelogram.
Special Quadrilaterals
- A square is always a rhombus.
- A quadrilateral is sometimes a parallelogram.
- A rectangle is sometimes a rhombus.
- A parallelogram with at least one right angle is sometimes a square.
- A trapezoid is never a parallelogram.
- A quadrilateral is sometimes a trapezoid.
- The bases of an isosceles trapezoid are never congruent.
- A parallelogram is sometimes a rectangle.
- A kite has congruent diagonals never.
Triangle Properties in Quadrilaterals
- Each diagonal of a parallelogram always divides it into two congruent triangles.
- A parallelogram whose diagonals are congruent and perpendicular to each other is always a square.
- A quadrilateral can sometimes be a parallelogram if its diagonals are perpendicular.
- The bases of a trapezoid are never congruent.
- Opposite angles of a parallelogram are sometimes supplementary.
- If the diagonals of a quadrilateral are perpendicular, the quadrilateral is sometimes a square.
- A diagonal of an isosceles trapezoid never divides it into two congruent triangles.
- A rhombus is sometimes equiangular.
- A quadrilateral with congruent angles is always a rectangle.
- If the diagonals of a square are drawn, the resulting four triangles are always isosceles right triangles.
- If the diagonals of a parallelogram bisect opposite angles, the parallelogram is sometimes a square.
Studying That Suits You
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Description
Test your knowledge on the unique properties of various quadrilaterals, including rectangles, rhombuses, and parallelograms. This quiz will challenge your understanding of sides, angles, and diagonals in these geometric shapes.
