Quiz Over Properties Of Parallelograms

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| By Mgarwood
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  • 1/10 Questions

    Which statement is true:

    • All quadrilaterals are rectangles
    • All rectangles are quadrilaterals
    • All rectangles are squares
    • All quadrilaterals are squares
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About This Quiz

This quiz assesses knowledge on properties of parallelograms, focusing on their characteristics within the broader context of quadrilaterals. It evaluates understanding of geometric definitions, relationships, and problem-solving skills relevant to parallelograms and related shapes.

Quiz Over Properties Of Parallelograms - Quiz

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  • 2. 

    Identify the quadrilateral which has one pair of parallel sides.

    • Kite

    • Trapezoid

    • Rectangle

    • Rhombus

    Correct Answer
    A. Trapezoid
    Explanation
    A trapezoid is a quadrilateral that has one pair of parallel sides. This means that two sides of the trapezoid are parallel while the other two sides are not. Therefore, the correct answer is trapezoid. A kite has two pairs of consecutive sides that are equal in length, a rectangle has four right angles and opposite sides that are equal in length, and a rhombus has four sides of equal length.

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  • 3. 

    If a quadrilateral is a parallelogram, then its consecutive angles are    ?  

    • Complementary

    • Congruent

    • Supplementary

    • Equal

    Correct Answer
    A. Supplementary
    Explanation
    If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. This is because in a parallelogram, opposite sides are parallel and opposite angles are congruent. Since consecutive angles are the ones that share a side, they are also opposite angles. Therefore, they are congruent and their measures add up to 180 degrees, making them supplementary.

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  • 4. 

    Parallelogram JKLM (pt O is diagonal intersection), angle KLO = 80, angle MLO = 40, find the measure of angle KJM

    Correct Answer
    120
    Explanation
    In a parallelogram, opposite angles are equal. Since angle KLO is 80 degrees and angle MLO is 40 degrees, angle KJM must also be 80 degrees in order for the opposite angles to be equal. However, since the sum of the angles in a triangle is 180 degrees, angle KJM must be 180 - 80 = 100 degrees. Therefore, the measure of angle KJM is 100 degrees, not 120 degrees.

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  • 5. 

    Which of these descriptions would NOT guarantee that the figure was a square?

    • A parallelogram with perpendicular diagonals

    • A quadrilateral with all right angles and all sides congruent

    • Both a rectangle and a rhombus

    • A quadrilateral with all sides and all angles congruent

    Correct Answer
    A. A parallelogram with perpendicular diagonals
    Explanation
    A parallelogram with perpendicular diagonals does not guarantee that the figure is a square because a rectangle can also have perpendicular diagonals. Therefore, this description can apply to both squares and rectangles, making it not a guarantee of a square.

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  • 6. 

    Isosceles trapezoid ABCD has legs AB and CD and base BC.  If AB = 3y - 9, BC =8y - 2 and CD = 7y - 10, find the value of y.

    Correct Answer
    .25
    1/4
    Explanation
    The given trapezoid is isosceles, which means that the lengths of the legs AB and CD are equal. Therefore, we can set up an equation: 3y - 9 = 7y - 10. Solving this equation, we get y = 1/4 or 0.25. Therefore, the value of y is 0.25 or 1/4.

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  • 7. 

    The four properties of the diagonals of squares are

    • Congruent to each other, congruent to the sides, bisect both sets of angles, bisect each other

    • Bisect each other, bisect one set of angles, are congruent to each other, are perpendicular to each other

    • Are congruent to each other, bisect both sets of angles, are perpendicular to each other, are twice the length of the sides

    • Are perpendicular to each other, bisect each other, bisect both sets of angles, are congruent to each other

    Correct Answer
    A. Are perpendicular to each other, bisect each other, bisect both sets of angles, are congruent to each other
    Explanation
    The answer states that the properties of the diagonals of squares are that they are perpendicular to each other, bisect each other, bisect both sets of angles, and are congruent to each other. This means that the diagonals of a square intersect at a right angle, divide each other into equal segments, divide the angles of the square into equal parts, and have the same length. These properties are unique to squares and help define their geometric characteristics.

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  • 8. 

    Which of these descriptions would NOT guarantee that a figure was a parallelogram?

    • A quadrilateral with consecutive angles supplementary

    • A quadrilateral with the diagonals bisecting each other

    • A quadrilateral with two opposite sides congruent

    • A quadrilateral with one pair of opposite sides both parallel and congruent

    Correct Answer
    A. A quadrilateral with two opposite sides congruent
    Explanation
    A quadrilateral with two opposite sides congruent does not guarantee that the figure is a parallelogram because a rhombus also has two opposite sides congruent, but it is not a parallelogram. A parallelogram requires that both pairs of opposite sides are congruent.

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  • 9. 

    Rhombus MATH, angle HMA = 100, find the measures of angles MTH and MAT

    Correct Answer
    50 and 80
    Explanation
    In a rhombus, opposite angles are equal. Since angle HMA is given as 100 degrees, angle MTH is also 100 degrees. Additionally, the sum of the angles in a rhombus is always 360 degrees. Since angle HMA is 100 degrees, the sum of angles MAT and MTH must be 360 - 100 = 260 degrees. Therefore, angle MAT is 260 - 100 = 160 degrees. Thus, the measures of angles MTH and MAT are 100 degrees and 160 degrees respectively.

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  • 10. 

    LMNP is a rectangle.  Find the value of x and the length of each diagonal. LN = 5x - 8 and MP = 2x + 1

    Correct Answer
    3, 9.9
    Explanation
    In a rectangle, the diagonals are equal in length. So, we have:
    LN = MP
    Substituting the given expressions for LN and MP, we get:
    5x - 8 = 2x + 1
    Solving this equation for x, we get:
    5x - 2x = 8 + 1
    3x = 9
    x = 9 / 3 = 3
    Now, substituting x = 3 into the expressions for LN and MP, we get:
    LN = 5(3) - 8 = 7
    MP = 2(3) + 1 = 7
    So, the length of each side of the rectangle is 7 units.
    The length of the diagonal (D) of a rectangle can be found using the Pythagorean theorem:
    D = sqrt(LN^2 + MP^2)
    Since LN = MP = 7, we get:
    D = sqrt(7^2 + 7^2) = sqrt(98) ≈ 9.9 units
    So, the length of each diagonal of the rectangle is approximately 9.9 units.

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  • Current Version
  • Feb 21, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Jan 06, 2010
    Quiz Created by
    Mgarwood
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