Mathematics: is rectangle PQRS going to rectangle WXYZ

is rectangle PQRS going to rectangle WXYZ, №13338812, 13.01.2023 12:00

Mathematics

**will give brainliest** given rectangles abcd and pqrs, and given that rectangle abcd is fully rotated about line bc, answer the following questions (using the diagram). a.) describe the figure generated by the rectangle rotating about line bc. b.) about which line could you rotate rectangle pqrs to generate a figure that is similar to the first solid? c.) what are the ratios of the surface areas and volumes of the solids generated from abcd and pqrs? d.) are abcd and pqrs golden rectangles? why or why not?

Step-by-step answer

P Answered by Specialist

7

A.rotation and a dilation of 1.25
B. PS
C.3:4
D.yes. They are similar

Mathematics

**will give brainliest** given rectangles abcd and pqrs, and given that rectangle abcd is fully rotated about line bc, answer the following questions (using the diagram). a.) describe the figure generated by the rectangle rotating about line bc. b.) about which line could you rotate rectangle pqrs to generate a figure that is similar to the first solid? c.) what are the ratios of the surface areas and volumes of the solids generated from abcd and pqrs? d.) are abcd and pqrs golden rectangles? why or why not?

Step-by-step answer

P Answered by Specialist

7

A.rotation and a dilation of 1.25
B. PS
C.3:4
D.yes. They are similar

Mathematics

Need . just need my answers checked. in advance. my answers are in brackets. 1. the coordinates of the vertices of δjkl are j(-5, -1) , k(0, 1) , and l(2, -5). which statement correctly describes whether δjkl is a right triangle? a. δjkl is a right triangle because jk is perpendicular to jl. b. δjkl is a right triangle because jl is perpendicular to kl. c. δjkl is a right triangle because jk is perpendicular to kl. [ d. δjkl is not a right triangle because no two of its sides are perpendicular. ] 2. the coordinates of the vertices of δjkl are j(0,

Step-by-step answer

P Answered by Specialist

6

#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

The coordinates of the vertices of quadrilateral pqrs are p(−4, 2) , q(3, 4) , r(5, 0) , and s(−3, −2) . which statement correctly describes whether quadrilateral pqrs is a rectangle? a. quadrilateral pqrs is not a rectangle because it has only one right angle. b. quadrilateral pqrs is not a rectangle because it has no right angles. c. quadrilateral pqrs is not a rectangle because it has only two right angles. d. quadrilateral pqrs is a rectangle because it has four right angles.

Step-by-step answer

P Answered by Master

12

a. Quadrilateral PQRS is not a rectangle because it has only one right angle.

Step-by-step explanation:

Mathematics

The coordinates of the vertices of quadrilateral pqrs are p(−4, 2) , q(3, 4) , r(5, 0) , and s(−3, −2) . which statement correctly describes whether quadrilateral pqrs is a rectangle? a. quadrilateral pqrs is not a rectangle because it has only one right angle. b. quadrilateral pqrs is not a rectangle because it has no right angles. c. quadrilateral pqrs is not a rectangle because it has only two right angles. d. quadrilateral pqrs is a rectangle because it has four right angles.

Step-by-step answer

P Answered by Master

12

a. Quadrilateral PQRS is not a rectangle because it has only one right angle.

Step-by-step explanation:

Mathematics

Need . just need my answers checked. in advance. my answers are in brackets. 1. the coordinates of the vertices of δjkl are j(-5, -1) , k(0, 1) , and l(2, -5). which statement correctly describes whether δjkl is a right triangle? a. δjkl is a right triangle because jk is perpendicular to jl. b. δjkl is a right triangle because jl is perpendicular to kl. c. δjkl is a right triangle because jk is perpendicular to kl. [ d. δjkl is not a right triangle because no two of its sides are perpendicular. ] 2. the coordinates of the vertices of δjkl are j(0,

Step-by-step answer

P Answered by Specialist

6

#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

The coordinates of the vertices of quadrilateral pqrs are p(−4, 2) , q(3, 4) , r(5, 0) , and s(−3, −2). which statement correctly describes whether quadrilateral pqrs is a rectangle? quadrilateral pqrs is not a rectangle because it has only one right angle. quadrilateral pqrs is not a rectangle because it has only two right angles. quadrilateral pqrs is a rectangle because it has four right angles. quadrilateral pqrs is not a rectangle because it has no right angles.

Step-by-step answer

P Answered by Specialist

56

Quadrilateral PQRS is not a rectangle because it has only one right angle.

Mathematics

Given: quadrilateral pqrs is a rectangle. prove: pr = qs reason statement 1. quadrilateral pqrs is a rectangle. given 2. rectangle pqrs is a parallelogram. definition of a rectangle 3.qp ≅ rs qr ≅ ps 4. m∠qps = m∠rsp = 90° definition of a rectangle 5. δ pqs ≅ δsrp sas criterion for congruence 6. pr ≅ qs corresponding sides of congruent triangles are congruent. 7. pr = qs congruent line segments have equal measures. what is the reason for the third step in this proof?

Step-by-step answer

P Answered by PhD

15

Step-by-step explanation:

Given: Quadrilateral PQRS is a rectangle.

To prove: PR = QS

Proof: 1. Quadrilateral PQRS is a rectangle(Given).

2. Rectangle PQRS is a parallelogram (Definition of a rectangle).

3. QP ≅ RS QR ≅ PS (Opposite angles of parallelogram are equal).

4. m∠QPS = m∠RSP = 90° (definition of a rectangle)

5. Δ PQS ≅ ΔSRP (SAS criterion for congruence)

6. PR ≅ QS (Corresponding sides of congruent triangles are congruent).

7. PR = QS (Congruent line segments have equal measures).

Mathematics

Given: quadrilateral pqrs is a rectangle. prove: pr = qs reason statement 1. quadrilateral pqrs is a rectangle. given 2. rectangle pqrs is a parallelogram. definition of a rectangle 3.qp ≅ rs qr ≅ ps 4. m∠qps = m∠rsp = 90° definition of a rectangle 5. δ pqs ≅ δsrp sas criterion for congruence 6. pr ≅ qs corresponding sides of congruent triangles are congruent. 7. pr = qs congruent line segments have equal measures. what is the reason for the third step in this proof?

Step-by-step answer

P Answered by PhD

15

Step-by-step explanation:

Given: Quadrilateral PQRS is a rectangle.

To prove: PR = QS

Proof: 1. Quadrilateral PQRS is a rectangle(Given).

2. Rectangle PQRS is a parallelogram (Definition of a rectangle).

3. QP ≅ RS QR ≅ PS (Opposite angles of parallelogram are equal).

4. m∠QPS = m∠RSP = 90° (definition of a rectangle)

5. Δ PQS ≅ ΔSRP (SAS criterion for congruence)

6. PR ≅ QS (Corresponding sides of congruent triangles are congruent).

7. PR = QS (Congruent line segments have equal measures).

Mathematics

Given: quadrilateral pqrs is a rectangle. prove: pr = qs reason statement 1. quadrilateral pqrs is a rectangle. given 2. rectangle pqrs is a parallelogram. definition of a rectangle 3.qp ≅ rs qr ≅ ps 4. m∠qps = m∠rsp = 90° definition of a rectangle 5. δ pqs ≅ δsrp sas criterion for congruence 6. pr ≅ qs corresponding sides of congruent triangles are congruent. 7. pr = qs congruent line segments have equal measures. what is the reason for the third step in this proof?

Step-by-step answer

P Answered by PhD

54

opposite sides in rectangle are congruent.

Step-by-step explanation:

It is given that Quadrilateral PQRS is a rectangle.

Since opposite sides of rectangle are congruent.

Therefore , QP ≅ RS, QR ≅ PS

Therefore, the reason for "QP ≅ RS, QR ≅ PS" in this proof is "opposite sides in rectangle are congruent."

hence, the reason for the third step in this proof is "opposite sides in rectangle are congruent."

is rectangle PQRS going to rectangle WXYZ

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