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Questions and Answers
Which property is unique to kites?
Which property is unique to kites?
- All angles are equal.
- The two non-parallel sides are congruent.
- Diagonals are perpendicular. (correct)
- The diagonals bisect each other.
What defines an isosceles trapezoid?
What defines an isosceles trapezoid?
- A trapezoid with supplementary angles on the same side of a leg.
- A trapezoid with all four sides of different lengths.
- A trapezoid with congruent legs. (correct)
- A trapezoid with two adjacent right angles.
What is a defining characteristic of a trapezoid?
What is a defining characteristic of a trapezoid?
- It is a quadrilateral with four sides of equal length.
- It has two pairs of opposite congruent angles.
- It has at least one pair of parallel sides. (correct)
- It always has right angles.
Which statement about trapezoids is always true?
Which statement about trapezoids is always true?
What is a key property of all parallelograms regarding their sides?
What is a key property of all parallelograms regarding their sides?
In the case of a quadrilateral where two pairs of sides are congruent and one pair of opposite angles is congruent, what is it most likely to be?
In the case of a quadrilateral where two pairs of sides are congruent and one pair of opposite angles is congruent, what is it most likely to be?
Which of the following shapes is a type of parallelogram?
Which of the following shapes is a type of parallelogram?
What defines the diagonals of a kite?
What defines the diagonals of a kite?
In trapezoids, what relationship exists between the angles formed between a leg and a base?
In trapezoids, what relationship exists between the angles formed between a leg and a base?
Which of the following statements is true about the diagonals of a parallelogram?
Which of the following statements is true about the diagonals of a parallelogram?
What is a characteristic of a square that differentiates it from other parallelograms?
What is a characteristic of a square that differentiates it from other parallelograms?
What is true about the angles in a rhombus?
What is true about the angles in a rhombus?
What defines a trapezoid as distinct from other quadrilaterals?
What defines a trapezoid as distinct from other quadrilaterals?
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Study Notes
Quadrilaterals
- Quadrilaterals are four-sided polygons with unique properties.
- There are two types of quadrilaterals: parallelograms and kites/trapezoids.
Parallelograms
- Characteristics
- Opposite sides are equal in length.
- Opposite angles are equal in measure.
- Consecutive angles are supplementary (add up to 180 degrees).
- Diagonals bisect each other.
- Examples
- Rectangle: A parallelogram with four right angles
- Square: A rectangle with all sides equal.
- Rhombus: A parallelogram with all sides equal.
Kites
- Characteristics
- Two pairs of adjacent sides are congruent (equal in length).
- Diagonals are perpendicular to each other.
- The longer diagonal bisects the shorter diagonal.
Trapezoids
- Characteristics
- Trapezoids have exactly one pair of parallel sides, called bases.
- The non-parallel sides are called legs.
- The angles on the same side of a leg are supplementary (add up to 180 degrees).
- The diagonals of a trapezoid intersect each other.
Types Of Trapezoids
- Isosceles Trapezoid: A trapezoid with congruent legs.
- Right Trapezoid: A trapezoid with two adjacent right angles.
- Scalene Trapezoid: A trapezoid with all four sides of different lengths.
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