Geometry - Properties of Parallelograms

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Questions and Answers

A quadrilateral with both pairs of opposite sides parallel is called a ______.

parallelogram

In a parallelogram, all four angles are congruent.

False (B)

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?

All angles are right angles (A) Signup and view all the answers

If two opposite angles of a quadrilateral are congruent, is it necessarily a parallelogram? Explain your answer.

No, it is not necessarily a parallelogram. While opposite angles being congruent is a property of parallelograms, other quadrilaterals can also have congruent opposite angles. Signup and view all the answers

In a parallelogram, consecutive angles are ______.

supplementary Signup and view all the answers

Which of the following conditions is sufficient to prove that a quadrilateral is a parallelogram?

One pair of opposite sides is congruent and parallel (D) Signup and view all the answers

Which of the following conditions is NOT a requirement for a quadrilateral to be a parallelogram?

All four angles are right angles. (D) Signup and view all the answers

If two opposite angles in a quadrilateral are congruent, then the quadrilateral must be a parallelogram.

True (A) Signup and view all the answers

What is the sum of two consecutive angles in a parallelogram?

180 degrees Signup and view all the answers

A parallelogram can be divided into two congruent ______ by drawing a diagonal.

triangles Signup and view all the answers

Match each property with the corresponding characteristic that guarantees a quadrilateral is a parallelogram:

Opposite sides are congruent = Two pairs of opposite sides are congruent. Opposite angles are congruent = The two sets of opposing angles are congruent. Diagonals bisect each other = The two diagonals bisect each other. Consecutive angles are supplementary = Any two angles that share the same side in a parallelogram are supplementary. Signup and view all the answers

Which of the following is TRUE about the diagonals of a parallelogram?

They always bisect each other. (D) Signup and view all the answers

If a quadrilateral has two pairs of congruent sides, it must be a parallelogram.

False (B) Signup and view all the answers

What is the term used to describe the point where the diagonals of a parallelogram intersect?

midpoint Signup and view all the answers

If a quadrilateral has two adjacent angles that are ______, then it must be a parallelogram.

supplementary Signup and view all the answers

The diagonals of a rhombus bisect each other.

True (A) Signup and view all the answers

Which of the following is NOT a characteristic of a rectangle?

All sides are congruent (C) Signup and view all the answers

In parallelogram RUBY, ∠R = 115°. What is the measure of ∠U?

65° Signup and view all the answers

A quadrilateral with two pairs of congruent sides is a ______.

parallelogram Signup and view all the answers

Match the special parallelograms to their defining characteristics:

Rhombus = All sides are congruent Rectangle = All angles are right angles Square = All sides are congruent and all angles are right angles Signup and view all the answers

If the diagonals of a quadrilateral bisect each other, what type of quadrilateral must it be?

Parallelogram (B) Signup and view all the answers

In parallelogram ROAD, RM = 2y - 1 and MA = y + 2. Solve for y.

y = 3 Signup and view all the answers

A parallelogram with one right angle is a square.

False (B) Signup and view all the answers

The diagonals of a rectangle are ______.

congruent Signup and view all the answers

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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Description

Test your knowledge on the properties and characteristics of parallelograms. This quiz covers key concepts including definitions, properties, and theorems related to parallelograms. Challenge yourself with questions that require both understanding and application of geometric principles.