prove that a rectangle has congruent diagonals, №9034361, 05.03.2022 22:32

Mathematics

Need , on level geometry 35 pts! let abcd be a rectangle with a on top left, b on top right, d on bottom left and c on the bottom right. prove that a rectangle has congruent diagonals.

Step-by-step answer

P Answered by PhD

2

A rectangle has congruent diagonals

Step-by-step explanation:

* Lets explain how to solve the problem

- In any rectangle each two opposite sides are parallel and equal

- All the angles of a rectangles are right angles

- To prove that the diagonals of a rectangle are congruent, we will use

the SAS case of congruent

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and

including angle in the 2nd Δ

* Lets solve the problem

∵ ABCD is a rectangle

∴ AD = BC

∴ AB = CD

∴ m∠A = m∠B = m∠C = m∠D = 90°

∵ AC and BD are the diagonals of the rectangle

- In the 2 triangles ADC and BCD

∵ AD = BC ⇒ opposite sides in a rectangle

∵ m∠ADC = m∠BCD ⇒ all angles are equal in the rectangle

∵ DC = CD ⇒ common side in the two triangles

∴ ΔADC ≅ ΔBCD ⇒ SAS

- From congruent

∴ AC = BD

∵ AC and BD are the diagonals of the rectangle

∴ The diagonals of the rectangle are congruent

* A rectangle has congruent diagonals

Mathematics

Need , on level geometry 35 pts! let abcd be a rectangle with a on top left, b on top right, d on bottom left and c on the bottom right. prove that a rectangle has congruent diagonals.

Step-by-step answer

P Answered by PhD

2

A rectangle has congruent diagonals

Step-by-step explanation:

* Lets explain how to solve the problem

- In any rectangle each two opposite sides are parallel and equal

- All the angles of a rectangles are right angles

- To prove that the diagonals of a rectangle are congruent, we will use

the SAS case of congruent

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and

including angle in the 2nd Δ

* Lets solve the problem

∵ ABCD is a rectangle

∴ AD = BC

∴ AB = CD

∴ m∠A = m∠B = m∠C = m∠D = 90°

∵ AC and BD are the diagonals of the rectangle

- In the 2 triangles ADC and BCD

∵ AD = BC ⇒ opposite sides in a rectangle

∵ m∠ADC = m∠BCD ⇒ all angles are equal in the rectangle

∵ DC = CD ⇒ common side in the two triangles

∴ ΔADC ≅ ΔBCD ⇒ SAS

- From congruent

∴ AC = BD

∵ AC and BD are the diagonals of the rectangle

∴ The diagonals of the rectangle are congruent

* A rectangle has congruent diagonals

Mathematics

Prove that a rectangle has congruent diagonals

Step-by-step answer

P Answered by Master

Look below

Step-by-step explanation:

Lets say there is a rectangle abcd

One way is: Triangle ABC is congruent to triangle DCB

Another way is: Since a rectangle is a parallelogram too, segment ab=dc. This is because opposite sides of a parallelogram are congruent.

Mathematics

Prove that a rectangle has congruent diagonals

Step-by-step answer

P Answered by Specialist

Look below

Step-by-step explanation:

Lets say there is a rectangle abcd

One way is: Triangle ABC is congruent to triangle DCB

Another way is: Since a rectangle is a parallelogram too, segment ab=dc. This is because opposite sides of a parallelogram are congruent.

Mathematics

Prove that a rectangle has congruent diagonals. be sure to create and name the appropriate geometric figures

Step-by-step answer

P Answered by PhD

18

The attached figure reprsents a prove that a rectangle has congruent diagonals.

Given: rectangle ABCD

Prove: BD ≅ AC

Prove that a rectangle has congruent diagonals. be sure to create and name the appropriate geometric

Mathematics

PLS HELP ME ASAP Hernando claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select all that apply. A) The rectangles are congruent since a reflection over the x-axis followed by a translation of 5 units to the right carries Rectangle 1 onto Rectangle 2. B) The rectangles are congruent since a translation of 6 units down and 7 units to the left carries Rectangle 1 onto Rectangle 2. C) The rectangles are congruent since a reflection over the x-axis followed by a translation of 7 units

Step-by-step answer

P Answered by PhD

1

C D E

Step-by-step explanation: they’re congruent

Mathematics

PLS HELP ME ASAP Hernando claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select all that apply. A) The rectangles are congruent since a reflection over the x-axis followed by a translation of 5 units to the right carries Rectangle 1 onto Rectangle 2. B) The rectangles are congruent since a translation of 6 units down and 7 units to the left carries Rectangle 1 onto Rectangle 2. C) The rectangles are congruent since a reflection over the x-axis followed by a translation of 7 units

Step-by-step answer

P Answered by PhD

1

C D E

Step-by-step explanation: they’re congruent

Mathematics

Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a rectangle? a coordinate plane with quadrilateral ABCD at A negative 2 comma 0, B 0 comma negative 2, C negative 3 comma negative 5, D negative 5 comma negative 3 Prove that segments AD and AB are congruent and parallel. Prove that opposite sides are congruent and that the slopes of consecutive sides are equal. Prove that segments BC and CD are congruent and parallel. Prove that opposite sides are congruent and that the slopes of consecutive sides

Step-by-step answer

P Answered by PhD

Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals

Step-by-step explanation:

In Quadrilateral ABCD with points A(-2,0), B(0,-2), C(-3,-5), D(-5,-3)

Using the distance formula

d = sqrt(x2-x1)^2+(y2-y1)^2

|AB| = sqrt(0-(-2))^2+(-2-0)^2 = sqrt(8) = 2sqrt(2)

|CD| = sqrt(-5+3))^2+(-3+5)^2) = sqrt(8) = 2sqrt(2)

|BC| = sqrt(-3-0))^2+(-5+2)^2 = sqrt(18) = 3sqrt(2)

|AD| sqrt(-5+2)^2+(-3-0)^2 = sqrt(18) = 3sqrt(2)

Since |AB| is congruent to |CD| and |BC| is congruent to |AD|, we conclude that opposite sides are congruent.

Next, let us consider the slope.

Slope of |AB| = _-2-0 =__-2__ = -1

0-(-2) 2

Slope of |BC| = __-5+2___ = _-3___ = 1

-3-0 -3

Since the slopes of consecutive sides are opposite reciprocals, therefore ABCD is a rectangle.

Mathematics

(04.01 LC) Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a rectangle? Prove that segments AD and AB are congruent and parallel. Prove that opposite sides are congruent and that the slopes of consecutive sides are equal. Prove that segments BC and CD are congruent and parallel. Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals

Step-by-step answer

P Answered by PhD

29

(D)Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals

Step-by-step explanation:

To use coordinate geometry to prove that quadrilateral ABCD is a rectangle. We prove that opposite sides are congruent in order to show equality of the lines.

We also show that the slopes of consecutive sides are opposite reciprocals, this is in order to show that the lines are perpendicular to one another.

The correct option is D.

Mathematics

HELP PLEASE 100 POINTS AND BRAINLIEST! Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a rectangle? a coordinate plane with quadrilateral ABCD at A negative 2 comma 0, B 0 comma negative 2, C negative 3 comma negative 5, D negative 5 comma negative 3 Prove that segments AD and AB are congruent and parallel. Prove that opposite sides are congruent and that the slopes of consecutive sides are equal. Prove that segments BC and CD are congruent and parallel. Prove that opposite sides are congruent

Step-by-step answer

P Answered by PhD

23

(D)Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals

Step-by-step explanation:

Let us verify the choosen option

In Quadrilateral ABCD with points A(-2,0), B(0,-2), C(-3,-5), D(-5,-3)

Using the distance formula

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

$|AB|=\sqrt{(0-(-2))^2+(-2-0)^2}=\sqrt{8}=2\sqrt{2}\\|CD|=\sqrt{(-5+3))^2+(-3+5)^2}=\sqrt{8}=2\sqrt{2}\\|BC|=\sqrt{(-3-0))^2+(-5+2)^2}=\sqrt{18}=3\sqrt{2}\\|AD|=\sqrt{(-5+2)^2+(-3-0)^2}=\sqrt{18}=3\sqrt{2}\\$

Since |AB| is congruent to |CD| and |BC| is congruent to |AD|, we conclude that opposite sides are congruent.

Next, let us consider the slope.

Slope of |AB|= $\frac{-2-0}{0-(-2)} =\frac{-2}{2}=-1$

Slope of |BC| $=\frac{-5+2}{-3-0} =\frac{-3}{-3}=1$

Since the slopes of consecutive sides are opposite reciprocals, therefore ABCD is a rectangle.

Option D is the correct option.

prove that a rectangle has congruent diagonals

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