Mathematics : asked on rach1314
 16.10.2022

Which quadrilateral can have only 2 sides that are parallel and only 2 sides that are the same length ?

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06.12.2021, solved by verified expert
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We have to determine which quadrilateral can have only 2 sides that are parallel and only 2 sides that are the same lengths.
We know that a quadrilateral is a closed shaped polygon that have 4 sides, 4 vertices and 4 angles.
We know that a trapezium is an quadrilateral with only two parallel sides and if we make the two non parallel sides equal then the criteria of the quadrilateral having 2 equal sides and 2 parallel sides is fullfiled.
Hence a quadrilateral that have 2 equal sides and 2 parallel sides is an iscoceles trapezium.
A figure is attached in the end for your reference.
Which quadrilateral can have only 2 sides that, №14935004, 16.10.2022 14:49
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Mathematics
Step-by-step answer
P Answered by Specialist

#1) d. ΔJKL is not a right triangle because no two of its sides are perpendicular; #2) -1/3, 3, -7, is, two of these slopes have a product of -1; #3) a. Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length; #4) 1, -1/6, 1, -2/5, is not, only one pair of opposite sides is parallel; #5) c. Quadrilateral PQRS is not a rectangle because it has only one right angle.

Step-by-step explanation:

#1) The slope of any line segment is found using the formula

m=\frac{y_2-y_1}{x_2-x_1}

For JK, this gives us (1-1)/(-5-0) = 0/-5 = 0.  For KL this gives us (1--5)/(0-2) = 6/-2 = -3.  For LJ this gives us (-5-1)/(2--5) = -6/7.  None of these slopes are negative reciprocals, so none of the angles are right angles and this is not a right triangle.

#2) The slope of JK is (2-1)/(0-3) = 1/-3 = -1/3.  The slope of KL is (1--5)/(3-1) = 6/2 = 3.  The slope of LJ is (2--5)/(0-1) = 7/-1 = -7.  Two of these slopes have a product of -1, 3 and -1/3.  This means they are negative reciprocals so this has a right angle; this means JKL is a right triangle.

#3) The slope of DE is (5-4)/(-2-2) = 1/-4 = -1/4.  The slope of EF is (4-0)/(2-0) = 4/2 = 2.  The slope of FG is (0-1)/(0--4) = -1/4.  The slope  of GD is (1-5)/(-4--2) = -4/-2 = 2.  Opposite sides have the same slope so they are parallel.

Next we use the distance formula to find the length of each side:

d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

Using our points, the length of DE is

\sqrt{(5-4)^2+(-2-2)^2}=\sqrt{1^2+(-4)^2}=\sqrt{1+16}=\sqrt{17}

The length of EF is

d=\sqrt{(4-0)^2+(2-0)^2}=\sqrt{4^2+2^2}=\sqrt{16+4}=\sqrt{20}

The length of FG is

d=\sqrt{(0-1)^2+(0--4)^2}=\sqrt{(-1)^2+(4)^2}=\sqrt{1+16}=\sqrt{17}

The length of GD is

d=\sqrt{(1-5)^2+(-4--2)^2}=\sqrt{(-4)^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}

Opposite sides have the same length and are parallel, so this is a parallelogram.

#4) The slope of AB is (-1-2)/(-4--1) = -3/-3 = 1.  The slope of BC is (2-1)/(-1-5) = 1/-6 = -1/6.  The slope of CD is (1--3)/(5-1) = 4/4 = 1.  The slope of DA is (-3--1)/(1--4) = -2/5.  Only one pair of opposite sides is parallel, so this is not a parallelogram.

#5) The slope of PQ is (2-4)/(-4-3) = -2/-7 = 2/7.  The slope of QR is (4-0)/(3-5) = 4/-2 = -2.  The slope of RS is (0--2)/(5--3) = 2/8 = 1/4.  The slope of SP is (-2-2)/(-3--4) = -4/1 = -4.  Only one pair of sides has slopes that are negative reciprocals; this means this figure only has 1 right angle, so it is not a rectangle.

Mathematics
Step-by-step answer
P Answered by Specialist

#1) d. ΔJKL is not a right triangle because no two of its sides are perpendicular; #2) -1/3, 3, -7, is, two of these slopes have a product of -1; #3) a. Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length; #4) 1, -1/6, 1, -2/5, is not, only one pair of opposite sides is parallel; #5) c. Quadrilateral PQRS is not a rectangle because it has only one right angle.

Step-by-step explanation:

#1) The slope of any line segment is found using the formula

m=\frac{y_2-y_1}{x_2-x_1}

For JK, this gives us (1-1)/(-5-0) = 0/-5 = 0.  For KL this gives us (1--5)/(0-2) = 6/-2 = -3.  For LJ this gives us (-5-1)/(2--5) = -6/7.  None of these slopes are negative reciprocals, so none of the angles are right angles and this is not a right triangle.

#2) The slope of JK is (2-1)/(0-3) = 1/-3 = -1/3.  The slope of KL is (1--5)/(3-1) = 6/2 = 3.  The slope of LJ is (2--5)/(0-1) = 7/-1 = -7.  Two of these slopes have a product of -1, 3 and -1/3.  This means they are negative reciprocals so this has a right angle; this means JKL is a right triangle.

#3) The slope of DE is (5-4)/(-2-2) = 1/-4 = -1/4.  The slope of EF is (4-0)/(2-0) = 4/2 = 2.  The slope of FG is (0-1)/(0--4) = -1/4.  The slope  of GD is (1-5)/(-4--2) = -4/-2 = 2.  Opposite sides have the same slope so they are parallel.

Next we use the distance formula to find the length of each side:

d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

Using our points, the length of DE is

\sqrt{(5-4)^2+(-2-2)^2}=\sqrt{1^2+(-4)^2}=\sqrt{1+16}=\sqrt{17}

The length of EF is

d=\sqrt{(4-0)^2+(2-0)^2}=\sqrt{4^2+2^2}=\sqrt{16+4}=\sqrt{20}

The length of FG is

d=\sqrt{(0-1)^2+(0--4)^2}=\sqrt{(-1)^2+(4)^2}=\sqrt{1+16}=\sqrt{17}

The length of GD is

d=\sqrt{(1-5)^2+(-4--2)^2}=\sqrt{(-4)^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}

Opposite sides have the same length and are parallel, so this is a parallelogram.

#4) The slope of AB is (-1-2)/(-4--1) = -3/-3 = 1.  The slope of BC is (2-1)/(-1-5) = 1/-6 = -1/6.  The slope of CD is (1--3)/(5-1) = 4/4 = 1.  The slope of DA is (-3--1)/(1--4) = -2/5.  Only one pair of opposite sides is parallel, so this is not a parallelogram.

#5) The slope of PQ is (2-4)/(-4-3) = -2/-7 = 2/7.  The slope of QR is (4-0)/(3-5) = 4/-2 = -2.  The slope of RS is (0--2)/(5--3) = 2/8 = 1/4.  The slope of SP is (-2-2)/(-3--4) = -4/1 = -4.  Only one pair of sides has slopes that are negative reciprocals; this means this figure only has 1 right angle, so it is not a rectangle.

Mathematics
Step-by-step answer
P Answered by Master

The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that  coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}

EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}

FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}

DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}

Slope formula,

m=\frac{y_2-y_1}{x_2-x_1}

Slope of DE,

m_1=\frac{4-5}{2+2}= \frac{-1}{4}

Slope of EF,

m_2=\frac{0-4}{0-2}= 2

Slope of FG,

m_3=\frac{1-0}{-4-0}= \frac{-1}{4}

Slope of DG,

m_4=\frac{1-5}{-4+2}= 2

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.


The coordinates of the vertices of quadrilateral defg are d(−2, 5) , e(2, 4) , f(0, 0) , and g(−4, 1
Mathematics
Step-by-step answer
P Answered by Master

The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that  coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}

EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}

FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}

DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}

Slope formula,

m=\frac{y_2-y_1}{x_2-x_1}

Slope of DE,

m_1=\frac{4-5}{2+2}= \frac{-1}{4}

Slope of EF,

m_2=\frac{0-4}{0-2}= 2

Slope of FG,

m_3=\frac{1-0}{-4-0}= \frac{-1}{4}

Slope of DG,

m_4=\frac{1-5}{-4+2}= 2

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.


The coordinates of the vertices of quadrilateral defg are d(−2, 5) , e(2, 4) , f(0, 0) , and g(−4, 1

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