Podcast
Questions and Answers
A quadrilateral with both pairs of opposite sides parallel is called a ______.
A quadrilateral with both pairs of opposite sides parallel is called a ______.
parallelogram
In a parallelogram, all four angles are congruent.
In a parallelogram, all four angles are congruent.
False (B)
Match the following properties with their corresponding quadrilateral type:
Match the following properties with their corresponding quadrilateral type:
Opposite sides are congruent = Parallelogram All angles are right angles = Rectangle All sides are congruent = Rhombus All sides are congruent and all angles are right angles = Square
Which of the following is NOT a property of a parallelogram?
Which of the following is NOT a property of a parallelogram?
If two opposite angles of a quadrilateral are congruent, is it necessarily a parallelogram? Explain your answer.
If two opposite angles of a quadrilateral are congruent, is it necessarily a parallelogram? Explain your answer.
In a parallelogram, consecutive angles are ______.
In a parallelogram, consecutive angles are ______.
Which of the following conditions is sufficient to prove that a quadrilateral is a parallelogram?
Which of the following conditions is sufficient to prove that a quadrilateral is a parallelogram?
Which of the following conditions is NOT a requirement for a quadrilateral to be a parallelogram?
Which of the following conditions is NOT a requirement for a quadrilateral to be a parallelogram?
If two opposite angles in a quadrilateral are congruent, then the quadrilateral must be a parallelogram.
If two opposite angles in a quadrilateral are congruent, then the quadrilateral must be a parallelogram.
What is the sum of two consecutive angles in a parallelogram?
What is the sum of two consecutive angles in a parallelogram?
A parallelogram can be divided into two congruent ______ by drawing a diagonal.
A parallelogram can be divided into two congruent ______ by drawing a diagonal.
Match each property with the corresponding characteristic that guarantees a quadrilateral is a parallelogram:
Match each property with the corresponding characteristic that guarantees a quadrilateral is a parallelogram:
Which of the following is TRUE about the diagonals of a parallelogram?
Which of the following is TRUE about the diagonals of a parallelogram?
If a quadrilateral has two pairs of congruent sides, it must be a parallelogram.
If a quadrilateral has two pairs of congruent sides, it must be a parallelogram.
What is the term used to describe the point where the diagonals of a parallelogram intersect?
What is the term used to describe the point where the diagonals of a parallelogram intersect?
If a quadrilateral has two adjacent angles that are ______, then it must be a parallelogram.
If a quadrilateral has two adjacent angles that are ______, then it must be a parallelogram.
The diagonals of a rhombus bisect each other.
The diagonals of a rhombus bisect each other.
Which of the following is NOT a characteristic of a rectangle?
Which of the following is NOT a characteristic of a rectangle?
In parallelogram RUBY, ∠R = 115°. What is the measure of ∠U?
In parallelogram RUBY, ∠R = 115°. What is the measure of ∠U?
A quadrilateral with two pairs of congruent sides is a ______.
A quadrilateral with two pairs of congruent sides is a ______.
Match the special parallelograms to their defining characteristics:
Match the special parallelograms to their defining characteristics:
If the diagonals of a quadrilateral bisect each other, what type of quadrilateral must it be?
If the diagonals of a quadrilateral bisect each other, what type of quadrilateral must it be?
In parallelogram ROAD, RM = 2y - 1 and MA = y + 2. Solve for y.
In parallelogram ROAD, RM = 2y - 1 and MA = y + 2. Solve for y.
A parallelogram with one right angle is a square.
A parallelogram with one right angle is a square.
The diagonals of a rectangle are ______.
The diagonals of a rectangle are ______.
Flashcards
Quadrilateral
Quadrilateral
A closed plane figure with four sides and four angles.
Convex Quadrilateral
Convex Quadrilateral
A quadrilateral where the diagonals intersect.
Parallelogram
Parallelogram
A quadrilateral with both pairs of opposite sides parallel.
Properties of Parallelogram
Properties of Parallelogram
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Opposite Sides
Opposite Sides
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Consecutive Angles
Consecutive Angles
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Diagonals
Diagonals
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Parallelogram Conditions
Parallelogram Conditions
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Opposite Angles Congruent
Opposite Angles Congruent
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Supplementary Adjacent Angles
Supplementary Adjacent Angles
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Diagonal Bisection
Diagonal Bisection
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Matching Triangles
Matching Triangles
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Opposite Sides Parallel
Opposite Sides Parallel
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Angle Relationships
Angle Relationships
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Congruent Opposite Angles
Congruent Opposite Angles
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Diagonal Midpoint
Diagonal Midpoint
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Rhombus
Rhombus
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Rectangle
Rectangle
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Square
Square
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Conditions for Parallelogram
Conditions for Parallelogram
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Supplementary Angles
Supplementary Angles
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Opposite Angles
Opposite Angles
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Diagonals of Parallelogram
Diagonals of Parallelogram
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Theorem of Right Angles
Theorem of Right Angles
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Study Notes
Quadrilaterals
- A quadrilateral is a closed plane figure with four sides and four angles.
- A convex quadrilateral has intersecting diagonals.
- A non-convex quadrilateral has non-intersecting diagonals.
- Parallel lines are lines that never intersect.
- Intersecting lines are lines that cross each other.
Parallelograms
- A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
- Opposite sides are congruent (equal in length).
- Opposite angles are congruent.
- Consecutive angles are supplementary (add up to 180 degrees).
- Diagonals bisect each other.
Special Parallelograms
- Rectangle: A parallelogram with four right angles.
- Rhombus: A parallelogram with four congruent sides.
- Square: A parallelogram with four congruent sides and four right angles.
- A trapezoid is a quadrilateral with at least one pair of parallel sides
- A trapezium is a quadrilateral with no parallel sides.
- A kite is a quadrilateral with two pairs of adjacent sides that are congruent.
Theorems
- Equal opposite sides are sufficient for a quadrilateral to be a parallelogram.
- A single pair of congruent and parallel sides is sufficient to classify a quadrilateral as a parallelogram.
- Diagonals that bisect each other are sufficient to identify a quadrilateral as a parallelogram.
- A quadrilateral with equal opposite angles is always a parallelogram.
- A quadrilateral with any two consecutive angles adding up to 180 degrees is a parallelogram.
Diagonals
- Diagonals of a parallelogram bisect each other.
- Diagonals of a square are perpendicular and equal in length
- Diagonals of a rectangle are equal in length
- Diagonals of a rhombus are perpendicular.
Properties of Special Parallelograms (Theorems)
- A square's diagonals are perpendicular and are equal in length.
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