Given the coordinates, determine whether PQR & XYZ are congruent


P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)


PQ=

XY=

QR=

YZ=

PR=

XZ=


Are the triangles congruent? If yes, explain your reasoning and write a congruence statement.

Answers

Answer 1

Answer:

The triangles are congruent

Step-by-step explanation:

Given

[tex]P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)[/tex]

Required

Determine if PQR = XYZ

To do this, we make use of distance formula.

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

For PQ:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (-3,7)[/tex]

So:

[tex]PQ = \sqrt{(-3-5)^2+(7-(-4))^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(7+4)^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(11)^2}[/tex]

[tex]PQ = \sqrt{64+121}[/tex]

[tex]PQ = \sqrt{185}[/tex]

For XY:

[tex](x_1,y_1) = (-2,-1)[/tex]

[tex](x_2,y_2) = (9,7)[/tex]

So:

[tex]XY = \sqrt{(9-(-2))^2+(7-(-1))^2}[/tex]

[tex]XY = \sqrt{(9+2)^2+(7+1)^2}[/tex]

[tex]XY = \sqrt{(11)^2+(8)^2}[/tex]

[tex]XY = \sqrt{121+64}[/tex]

[tex]XY = \sqrt{185}[/tex]

For QR:

[tex](x_1,y_1) = (-3,7)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]QR = \sqrt{(0-(-3))^2 + (2-7)^2}[/tex]

[tex]QR = \sqrt{(0+3)^2 + (-5)^2}[/tex]

[tex]QR = \sqrt{(3)^2 + 25}[/tex]

[tex]QR = \sqrt{9 + 25}[/tex]

[tex]QR = \sqrt{34}[/tex]

For YZ:

[tex](x_1,y_1) = (9,7)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]YZ = \sqrt{(3-9)^2+(2-7)^2}[/tex]

[tex]YZ = \sqrt{(-6)^2+(-5)^2}[/tex]

[tex]YZ = \sqrt{36+25}[/tex]

[tex]YZ = \sqrt{61}[/tex]

For PR:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]PR = \sqrt{(0-5)^2+(2-(-4))^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(2+4)^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(6)^2}[/tex]

[tex]PR = \sqrt{25+36}[/tex]

[tex]PR = \sqrt{61}[/tex]

For XZ:

[tex](x_1,y_1) = (-2,-1)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]XZ = \sqrt{(3-(-2))^2+(2-(-1))^2}[/tex]

[tex]XZ = \sqrt{(3+2)^2+(2+1)^2}[/tex]

[tex]XZ = \sqrt{5^2+3^2}[/tex]

[tex]XZ = \sqrt{34}[/tex]

From the calculations above:

[tex]PQ = XY = \sqrt{185[/tex]

[tex]QR = XZ = \sqrt{34[/tex]

[tex]PR = YZ = \sqrt{61[/tex]

Hence, the triangles are congruent base on SSS (Sides- Sides-Sides)


Related Questions

Brainliest Question Of The Day:

Chen is making some bread, his brother, sister, little brother ate some bread. they ate 15 bread altogether. there was 7 loafs left. how many bread did Chen made?


Hint: 1 loaf has 12 pieces of bread


Correct answer for brainliest:)

Answers

Answer:

9?

Step-by-step explanation:

They ate 15 bread..

so if 1 loaf = 12 pc of bread,

they ate 1 loaf and 3 peace’s of another loaf.

their was still 7loafs left so he made

9 loafs if their was 7 whole lofs left, becasue they cut them into peace’s of bread?

12x-20=n(3x-5) what does n equal​

Answers

The answer is 4 do you need a step by step explanation or no
the answer is 4 because 12x-20 =4(3x-5)

Evaluate 1/3 to the power of 3

Answers

The answer is 0.0369 (4 d.p)
Take 1/3 and convert to a decimal which is 0.333. Then put the decimal to the power of 3. In which you will get 0.0369 if you change to a fraction it will be 369/1000.
Hope it helps.

If two parents, one with brown eyes (a dominant trait) and the other with blue eyes (the recessive trait) produce one twin boy with blue eyes, what is the probability that a fraternal twin will transmit the blue eye allele to his or her offspring

Answers

Answer:

50 percent

Step-by-step explanation:

It is given that one of the parent with a dominant trait have brown eyes and the other parent with a recessive trait has blue eyes. They produce a twin boy with eyes that is blue in color. So the probability of the fraternal twin to transmit his allele of blue eye to his or her offspring is 50 percent.

And also the probability of the offspring to pass the allele on to his or her offspring is 50 %.

The product rule is used : 0.5 x 0.5 = 0.25 or 25%.

Solve the following equation algebraically: 5x2 = 60

a. x~ +3 46
b. x~3.46
c. x = 12
d. X = +12​

Answers

Answer:

x = 3.46

Step-by-step explanation:

In this question, you have to solve the equation.

Solve:

5x² = 60

Divide both sides by 5.

x² = 12

In order to eliminate the exponent, you would square root both sides.

√x² = √12

x = √12

√12 = 3.4641..

x = 3.46

Your final answer would be x = 3.46

PLEASE help me. thank you

Answers

Answer:

Each paper weight is half a pound

Step-by-step explanation:

NEED HELP!!! I’ll report if your putting random answers down

Answers

Answer:

First blank: 8

Second Blank: 16

Third Blank: 56

Step-by-step explanation: Hope I helped

8, 16, 56
7*8= 56
5*8 + 2*8
40+ 16
56

if there where 10 apples and my frend took 6 how many do i have

Answers

Answer:

10-6=4

if your friend took 6 apples out of the 10 you have you would have 4 left.

Step-by-step explanation:

About how many more jazz records were sold in April than in February?

Answers

Answer: DO you have a chart or something that i can actually help you with

Step-by-step explanation:

A clothing company produced 600 items of clothing. Of those, 15% were jackets, 25% were dresses, and 15% were shoes. How many of the items of clothing were NOT jackets, dresses, or shoes?

Answers

Answer:

270 items

Step-by-step explanation:

Answer:

270 of them were not jackets dresses or shoes

Step-by-step explanation:

Part C
Use an exponential expression to calculate the area covered by purple loosestrife 7 years from now.

Answers

Answer:500(1.2)^x

Plato :)

Answer:

3

Step-by-step explanation:

PLATO

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Answers

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line X

Step-by-step explanation:

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Answers

Answer:

a=7b=9c=4

Step-by-step explanation:

Which statement is true about the line whose equation is y=-2x-5?
(1) it’s slope is -2
(2)it’s parallel to the line whose equation is y=-2x+5
(3) it’s y intercept is -5
(4)it’s perpendicular to the line whose
Equation is y=1/2x-5

Answers

Answer:

2

Step-by-step explanation:

I think dont come at me if I'm wrong

Answer:

1, 3, and 4 are true

Step-by-step explanation:

1. y=mx+b, m is the slope

2.  Parallel lines have the same slope. -2 is not equal to 2

3. y=mx+b, b is the y-intercept

4. Perpendicular lines,

If you multiply the slopes and the result is -1.

-2 times 1/2

-1

What is the solution to the linear equation 2/3 x - 1/2 = 1/3 + 5/6x

Answers

Answer:

Simplify and solve and get x=-5

Step-by-step explanation:

2/3x - 1/2= 1/3 + 5/6x

2/3x - 5/6x= 1/3 + 1/2

-1/6x= 5/6

x=-5

Which is the correct answer? and how can you find the answer

Answers

Answer:

?

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

-10/2=-5-7=-12

-8/2=-4-7=-11

Braniliest?

Based on the 2017 season, the Houston Astros have a winning percentage of .623. Use the binomial model to find the probability that the Astros will win 4 of their next 6 games.

P
(
x
)
=
[
n
!
x
!
(
n

x
)
!
]
p
x
q
n

x
A.
12.4%

B.
24.7%

C.
32.1%

D.
62.3%

Answers

Answer: Your answer would be C) 32.1%

Step-by-step explanation:

With the number of successes needed to be 4 and the total amount of trials (games) for this to be achieved in being 6 you can calculate a percentage based on their currenting winning percentage of .623 (don't forget decimals can be percentages, just move the decimal point over) and you can input all of this into the binomial model equation to get your answer. Please do note also that it would be a different answer entirely if you were to use .500 (50%) as a winning percentage which would be the logical conclusion as any team has a 50/50 chance of winning a given game but instead the question is asking us to calculate this percentage off the already given winning percentage. After inputting the data into the model formula you can conclude the answer to be 32.1% chance of them winning 4 out of the next 6 games. I hope this has been of assistance to you :)

Have a wonderful rest of your day!

5. Si un paquete de 100 hojas iguales mide 1 cm de altura, ¿cuál


es el grosor de una hoja?

Answers

Responder:

0,01 cm

Explicación paso a paso:

Dado que :

Un paquete de 100 hojas iguales = 1cm de alto

Esto significa que el grosor del paquete es de 1 cm de alto.

Dado que las hojas son iguales, el grosor de una sola hoja será:

(Espesor del paquete completo / número de hojas en el paquete)

(1 cm / 100)

= 0,01 cm

Usando proporciones, se encuentra que el grosor de una hoja es de 0.01 cm.

Esto problema é solucionado por proporciones, se utilizando de una regla de três.

Hay 100 hojas iguales, al todo midiendo 1 cm de altura. ¿Cuál es la equivalente medida de 1 hoja?

La regla de três es dada por:

100 hojas - 1 cm

1 hoja - x cm

Aplicando multiplicación cruzada:

[tex]100x = 1[/tex]

[tex]x = \frac{1}{100}[/tex]

[tex]x = 0.01[/tex]

Por eso, el grosor de una hoja es de 0.01 cm.

Un problema similar, que también envolve proporciones, es dado en https://brainly.com/question/24615636

An individual rides a bike at a rate of 15 miles per hour for h hours. Write an equation that expresses the situation, let x be the independent variable and y be the dependent variable.

Answers

Answer:

15y+x

Step-by-step explanation:

Isabelle is plotting a pentagon on a grid. So far, she has plotted and connected the three points shown on the grid below.

On a coordinate plane, lines connect points (negative 2, 4), (negative 3, 2), and (0, negative 2).

To complete the pentagon, she can choose only from the points below.

(2, 0), (–2, 0), (–2, 4), (2, 4)

How can Isabelle complete her pentagon?
Connect the point already at (0, –2) to a new point at (2, 0), and then connect
( 2, 0) to (–2, 4).
Connect the point already at (0, –2) to a new point at (–2, 0), and then connect ( –2, 0) to (–2, 4).
Connect the point already at (0, –2) to a new point at (–2, 0), connect ( –2, 0) to (2, 4), and then connect (2, 4) to (–2, 4).
Connect the point already at (0, –2) to a new point at (2, 0), connect
(2, 0) to (2, 4), and then connect (2, 4) to (–2, 4).

Answers

Answer:

D

Step-by-step explanation:

Connect the point already at (0, –2) to a new point at (2, 0), connect

(2, 0) to (2, 4), and then connect (2, 4) to (–2, 4).

Im pretty sure

Answer:

D

Step-by-step explanation:

if 50% is 100 what is 25%, 75%, and 100%​

Answers

Step-by-step explanation:

25%=50

75%=150

100%=200

hope it helps

mark me brainliest

find the measusre of the angles.

Answers

Answer:

1, 3, 5 =117

2, 4, 6, 7= 63

Step-by-step explanation:

Since we know that one angle is 117 degrees, 5, 1 and 3 will also be 117. 2, 4, 6 and 7 will also be the same. 117 plus 117 is 234. 63 + 63 = 126. 234+ 126 = 360.

A cell phone is originally priced at $80. The online retailer gives a discount and the cell phone is now priced at $40. Enter the percentage discount for the cost of the cell phone.

Answers

Answer: The percent that the phone is on sale is 50%. The discount if 40 dollars.1/2 of the total will be taken off.

j - 2.5 = 93.9
What is the value of j?

Answers

Answer:

j = 96.4

Step-by-step explanation:

Step-by-step explanation:

j - 2.5 = 93.9

j=93.9+2.5

j=96.4

Which of the following best estimates the sum 1/2+1/3
a 0.4
b .5
c .8
D 1.1

Answers

Hey! The answer is 0.8 or C
The answer is c. 1/2 is 0.5 and 1/3 is 0.33 so the sum is about 0.8

Daniel buys two apples for every five oranges. If you bought 12 apples, how many oranges dis he buy?

Answers

Answer:

30 oranges

Step-by-step explanation:

2 apples : 5 oranges

12 apples : 30 oranges

because 12 apples is 6 times the original ratio, so we multiply the 5 oranges by 6 too.

Jonah teachers pet training classes at the happy tails doggie daycare yesterday he talk to tricks to a group of dogs during a 30 minute class Jonah decided to create a longer class lasting 75 minutes if he teaches tricks at the same rate how many tricks with Jonah teach during the 75 minute class

Answers

Answer:

5

Step-by-step explanation:

he teaches 1 trick every 15 minutes 75 divided by 15 gives you 5 so Jonah can teach 5 tricks in a 75 minute class

Answer:

5

Step-by-step explanation:

 bjhugvcyfxtdrzstxycfugiholiugkyftdrsetdfyugi

What is the range of the mapping?

Answers

The range of the mapping is 1,4

Which equation can be used to determine the number of movie tickets sold if the cost of each ticket x was $5.50, and $6,850 was earned on the ticket sales?

Answers

Answer:

5.50x = 6,850

Step-by-step explanation:

Each ticket costs $5.50, and the total is $6,850.

Hope this helps! :)

If a person weighs 130 Ibs and they lose 1/10 of their weight.How much weight was lost

Answers

Answer:

13 lbs

Step-by-step explanation:

to find 1/10 we divide by 10

This can be found by moving the decimal back by one

So 130/10=13

13 lbs were lost

The person lost 13 lbs of weight.

What is weight?

Weight is the measure of how heavy an object is. Weight is measured in standard customary units. The mass of an object is the amount of material it contains.

Given that, the person weight=130 lbs and he lost 1/10 of his weight.

We need to find how much weight was lost.

Now, weight lost [tex]=\frac{1}{10} \times 130=13[/tex] lbs.

Hence, the person lost 13 lbs of weight.

To learn more about the weight visit:

https://brainly.com/question/10069252.

#SPJ2

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