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Quizzes > High School Quizzes > Mathematics

Properties of Parallelograms Practice Quiz

Boost geometry mastery with rectangle and parallelogram worksheets

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art promoting the interactive Shape Savvy Challenge, a middle school math quiz.

What is a parallelogram?
A triangle with equal sides
A quadrilateral with one pair of parallel sides
A quadrilateral with two pairs of parallel sides
A polygon with all right angles
A parallelogram is defined as a quadrilateral with two pairs of parallel sides. This property ensures that both pairs of opposite sides are congruent and parallel.
Which of the following is a necessary property of parallelograms?
All sides are equal
Diagonals are equal
They have four right angles
Opposite angles are congruent
In all parallelograms, opposite angles are congruent, which is a defining property. Other properties like equal diagonals or equal sides are specific to special types of parallelograms.
If a quadrilateral has both pairs of opposite sides parallel, which shape does it definitely represent?
Parallelogram
Kite
Square
Trapezoid
A quadrilateral with both pairs of opposite sides parallel meets the definition of a parallelogram. While a square is a type of parallelogram, the general shape is classified as a parallelogram.
In a parallelogram, what is true about the opposite sides?
They are equal in length
They are perpendicular
They intersect at right angles
They are coincident
One of the key characteristics of parallelograms is that each pair of opposite sides is equal in length. This property is fundamental in distinguishing parallelograms from other quadrilaterals.
Which shape is always considered a parallelogram?
Circle
Trapezoid
Rectangle
Triangle
A rectangle has both pairs of opposite sides parallel and equal, meeting the definition of a parallelogram. Other shapes do not necessarily have the required properties.
Which of the following statements is true about the diagonals in a parallelogram?
They always lie on the same line
They always bisect each other
They intersect at right angles
They are always equal in length
In any parallelogram, the diagonals intersect at their midpoints, meaning they bisect each other. The other statements are not generally true for all parallelograms.
A parallelogram has sides of lengths 8 cm and 5 cm. What additional property does it always have?
All sides are 5 cm
Both diagonals are 8 cm
Opposite sides are equal in length
The perimeter is 20 cm
One fundamental property of parallelograms is that opposite sides are equal in length. Thus, if one side is 8 cm, the side opposite to it is also 8 cm, and similarly for the 5 cm side.
If one angle in a parallelogram is 70°, what is the measure of its adjacent angle?
70°
90°
110°
140°
Consecutive angles in a parallelogram are supplementary, meaning they add up to 180°. Therefore, if one angle is 70°, its adjacent angle must be 110°.
If one angle in a parallelogram is 120°, what are the measures of the remaining three angles?
60°, 60°, 60°
60°, 120°, 60°
90°, 90°, 90°
120°, 60°, 60°
In a parallelogram, opposite angles are equal and consecutive angles are supplementary. With one angle as 120°, the adjacent angles are 60° (since 120° + 60° = 180°) and the angle opposite is also 120°, leaving the fourth angle as 60°.
Which formula correctly calculates the area of a parallelogram?
2 Ã - (Base + Height)
(Base + Height) ÷ 2
Base à - Side Length
Base à - Height
The area of a parallelogram is found by multiplying the base by its corresponding height. The other formulas do not correctly represent the method for calculating area.
What is the relationship between the diagonals and angles in a parallelogram?
Diagonals bisect each other
Diagonals are parallel to the sides
Diagonals always form right angles with the sides
Diagonals bisect the interior angles
In every parallelogram, the diagonals intersect and bisect each other. This is a defining property that helps distinguish parallelograms from other quadrilaterals.
Which condition distinguishes a rectangle from a general parallelogram?
Opposite sides are parallel
Diagonals bisect each other
Diagonals are equal in length
Opposite angles are equal
While all parallelograms have parallel opposite sides and diagonals that bisect each other, only rectangles have equal diagonals. This property is used to differentiate rectangles from other parallelograms.
A parallelogram has a base of 10 cm and a height of 6 cm. What is its area?
60 cm²
60 cm³
100 cm²
16 cm²
The area of a parallelogram is calculated using the formula Base à - Height. Multiplying 10 cm by 6 cm gives 60 cm², which is the area of the parallelogram.
What happens to the area of a parallelogram if the base is doubled while the height remains constant?
The area is halved
The area is doubled
The area remains the same
The area is quadrupled
Since the area of a parallelogram is the product of the base and the height, doubling the base while keeping the height constant will double the area.
Which statement is true about the midpoints of the sides of a parallelogram?
They form another parallelogram
They form a rectangle
They form a kite
They form an irregular quadrilateral
Connecting the midpoints of the sides of a parallelogram results in another parallelogram, known as the Varignon parallelogram. This inner parallelogram has properties derived from the original shape.
In a parallelogram with side lengths a and b and with angle A = θ, the length of diagonal AC (which does not include angle A) is given by which formula?
√(a² + b² - 2ab cosθ)
√(a² + b²)
√(a² + b² + 2ab cosθ)
a + b
Diagonal AC is found in triangle ABC where the included angle is 180° - θ. Using the Law of Cosines and the identity cos(180° - θ) = -cosθ, the formula simplifies to √(a² + b² + 2ab cosθ).
A parallelogram has an area of 84 square units and a base of 12 units. What is the height corresponding to that base?
7 units
6 units
8 units
10 units
The area of a parallelogram is calculated as Base à - Height. Dividing the area (84) by the base (12) yields a height of 7 units.
In a parallelogram, if one angle is three times its adjacent angle, what are the measures of all four angles?
90°, 90°, 90°, 90°
45°, 135°, 45°, 135°
60°, 120°, 60°, 120°
30°, 150°, 30°, 150°
Let the adjacent angles be x and 3x. Since they are supplementary, x + 3x = 180° leads to x = 45° and 3x = 135°. The opposite angles are equal, resulting in angles of 45°, 135°, 45°, and 135°.
The diagonals of a parallelogram measure 16 cm and 30 cm and intersect at an angle of 45°. What is the area of the parallelogram?
120√2 square units
240√2 square units
120 square units
240 square units
The area of a parallelogram can be found using the formula: Area = ½ à - (diagonal1) à - (diagonal2) à - sin(angle between diagonals). Substituting the values gives ½ à - 16 à - 30 à - sin45° = 120√2 square units.
In a parallelogram with sides of 13 cm and 5 cm, if one of its diagonals is 14 cm, what is the cosine of the angle between the two adjacent sides forming that diagonal?
-1/65
-13/5
13/5
1/65
Using the Law of Cosines in the triangle formed by the sides of lengths 13 cm, 5 cm, and the diagonal of 14 cm, we set up the equation: 14² = 13² + 5² - 2(13)(5) cosθ. Solving for cosθ yields -1/65, indicating an obtuse angle between the sides.
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Study Outcomes

  1. Understand and define the key properties of parallelograms.
  2. Analyze geometric diagrams to accurately identify parallelograms.
  3. Apply parallelogram properties to solve shape-related mathematical problems.
  4. Evaluate relative attributes of different quadrilaterals to distinguish parallelograms.
  5. Justify decisions using logical reasoning based on geometric principles.

Parallelograms Properties Worksheet Cheat Sheet

  1. Opposite Sides are Equal and Parallel - In a parallelogram, both pairs of opposite sides are congruent in length and run exactly parallel. This means if one side measures 5 cm, its opposite will too, creating a perfectly balanced shape. Try sketching one yourself and measure with a ruler to see the symmetry in action! Properties of Parallelograms
    2. MathPlanet
  2. Opposite Angles are Equal - Angles across from each other in a parallelogram match exactly, so a 60° corner always has a fellow 60° opposite it. This ensures rotational symmetry, making it easier to spot missing angles in problems. Grab a protractor and test out your own parallelogram drawing! Properties of Parallelograms
    3. MathPlanet
  3. Consecutive Angles are Supplementary - Any two neighboring angles in a parallelogram add up to 180°, becoming the perfect straight-line duo. So if one angle is 70°, the one next to it must be 110°. Practise measuring adjacent angles on different shapes to master this relationship! Properties of Parallelograms
    4. MathPlanet
  4. Diagonals Bisect Each Other - The diagonals of a parallelogram cross exactly at their midpoint, splitting each other into two equal halves. This midpoint magic is a powerful proof technique for identifying parallelograms. Draw one and mark the intersection to see how it always centers perfectly! Parallelogram Properties
    5. GeeksforGeeks
  5. Area Calculation - To find a parallelogram's area, multiply its base by its height (the perpendicular distance to the opposite side). An 8 cm base and 5 cm height give you 40 cm² - just like laying tiles on a floor! Try measuring everyday objects to reinforce this handy formula. Parallelogram Area Formula
    6. GeeksforGeeks
  6. Perimeter Formula - The perimeter of a parallelogram is 2 × (length + width). With a 6 cm length and a 4 cm width, the perimeter wraps around to 20 cm - perfect for fencing or framing designs. Practice by calculating perimeters of different parallelograms you draw! Parallelogram Perimeter
    7. GeeksforGeeks
  7. Diagonals Form Congruent Triangles - Each diagonal cuts the parallelogram into two congruent triangles, identical in shape and size. This congruency is a quick trick for solving many geometry problems, like finding unknown side lengths. Sketch both diagonals to reveal your matching triangles! Diagonal Triangle Trick
    8. MathPlanet
  8. Parallelogram Law - The sum of the squares of all four sides equals the sum of the squares of the two diagonals. This elegant relationship shows up in physics and vector math, going beyond simple shape facts. Plug in random numbers to see this law work its magic! Parallelogram Law
    9. Wikipedia
  9. Special Types of Parallelograms - Rectangles, rhombuses, and squares are all part of the parallelogram family: rectangles boast right angles, rhombuses have equal sides, and squares combine both perks. Recognizing these special cases helps you classify shapes in a flash. Draw each type and note what makes it unique! Parallelogram Family
    10. Cuemath
  10. Sum of Interior Angles - All four interior angles of a parallelogram add up to 360°, the hallmark of every quadrilateral. This simple angle arithmetic is key to solving angle puzzles and design challenges. Sketch and label angles on different parallelograms to lock it in your memory! Interior Angle Sum
    11. Cuemath
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