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3 years ago

Each of the following statements describes a quadrilateral. Which of the quadrilaterals are NOT parallelograms? (Pick 3)

Mathematics

2 answers:

Tanya [424]3 years ago

5 0

Answer:

Quadrilaterals 1, 2 and 4 does not represents a parallelogram.

Step-by-step explanation:

We know that, a parallelogram is a simple quadrilateral that have two opposite sides congruent.

Now, according to the options:

1. A parallelogram does not have congruent diagonals without having right angles.

2. A parallelogram does not have consecutive sides equal without being a rhombus.

3. A rectangle is a parallelogram which have both the diagonals of equal length. So, this quadrilateral might represents a rectangle, which is a parallelogram.

4. No two opposite angles of a parallelogram are right angles without the quadrilateral being a rectangle.

5. A rhombus is a parallelogram which have both the diagonals bisecting each other perpendicularly. So, this quadrilateral might represents a rhombus, which is a parallelogram.

Hence, we see that options 1, 2 and 4 does not represents a parallelogram.

kherson [118]3 years ago

3 0

Answer:

Options: Quadrilateral 1: The diagonals are congruent, but the quadrilateral has no right angles.

Quadrilateral 2: Two consecutive sides are congruent, but the figure is not a rhombus.

Quadrilateral 4: Two opposite angles are right angles, but the quadrilateral is not a rectangle.

Step-by-step explanation:

In a quadrilateral, the two sides are parallel to each other. This means that the two opposite sides are always equal. In a quadrilateral, the two sides are opposite and equal. In addition, one diagonal is perpendicular bisector of the other. This is true for all the quadrilaterals particularly parallelograms.

In the analysis of the factors above, the options 1, 2 and 4 do not apply.

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere. He

dezoksy [38]

Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

In the question, we are given that a sphere and a cylinder have the same radius and height.

We assume the radius of the sphere to be r, and its height to be h.

Now, the height of a sphere is its diameter, which is twice the radius.

Thus, the height of the sphere, h = 2r

Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.

The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.

Thus, the volume of the given sphere using the formula is (4/3)πr³.

The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.

Now, to compare the two volumes we take their ratios, as

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= {(4/3)πr³}/{2πr³}

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Thus, the volume of the sphere/the volume of the cylinder = 2/3,

or, the volume of the sphere = (2/3)*the volume of the cylinder.

Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.

Thus, Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

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For the complete question, refer to the attachment.

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