The perimeter of triangle ABC is 138 cm and BC || DE. Is triangle ABC = triangle ADE? Which conjecture supports your conclusion?

please help me it’s due in 30 minutes!!

The Perimeter Of Triangle ABC Is 138 Cm And BC || DE. Is Triangle ABC = Triangle ADE? Which Conjecture

Answers

Answer 1

Answer

yes triangle ABC is equal to triangle ADE

Step-by-step explanation:

x=46 cm, I got this after simplifying the equation of triangle ABC, x+4+x-4+x=138 cm, so this equation simplifies to 3x as +4-4 cancels out and there're 3 x's, so divide 138 by 3 and you get 46 cm, so AB is 50 cm, BC is 42 cm, and AC is 46 cm, this means EA is equal to EC, now here come a property of equality, EC attaches 2 parallel lines, as does DB, this means these 2 lines are transversals, so a number of angles are equal as well, corresponding angles are congruent, a.k.a equal to each other along with alternate interior angles, so since line DB AND line EC are transversals, we can deduce angle ADE is congruent to angle ABC, and angle DEA is equal to ACB, this mean we have 2 congruent angles, and 1 congruent set of sides, this mean that the 2 triangles are congruent due to Angle Angle Side, if your teacher doesn't use these terms, look it up, but the answer in short is yes, they are congruent or equal

Answer 2

We proved that ABC = triangle ADE by the concept of vertically opposite angles and given perimeter.

What is congruency?

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

We know when a transversal intersects two parallel lines vertically opposite angles are equal hence DE CB.

Given, (x + 4) + x + (x - 4) = 138.

3x = 138.

x = 46.

Now, BC = ED = (46 - 4) = 42 cm.

Assuming DA to be y.

∴ 46 + 42 + y = 138.

y = 50

And AB = x + 4 = 50 hence proving triangle ABC = triangle ADE.

learn more about congruency here :

https://brainly.com/question/7888063

#SPJ2


Related Questions

there are 678 freshmen ,and 552 sophomore students. how many more freshmen than sophomore students are there?​

Answers

Answer: There is 126 more freshmen than sophomores.

Step-by-step explanation:

Subtract the number of freshmen by the number of sophomores.

678 - 552 = 126

Just subtract 678-552
Which equals 126
There are 126 more freshmen than sophomore students

Please help i’m having a hard time answering it

Answers

So we know 5ft to 1cm then
4x5=20ft
6x5=30ft

Which rule describes the transformation?

Answers

I think its (x,y-(-x,-y)

Janelle would like to give a party bag to every person who is coming to her party. The cost of the party bag is $7 per person. Write an inequality that describes the number of people P that she can invite if Janelle has No more than $95 dollars to spend on the party bags.

Answers

Answer: Inequality that describes the number of people P that she can invite if Janelle has No more than $95 dollars to spend on the party bags: 7P  ≤  95  

Step-by-step explanation:

Given: The cost of the party bag is $7 per person.

P represents the number of people that she can invite.

Total cost for P people = ( cost per person) x (P)

=$ 7P   (i)

If  Janelle has No more than $95 dollars to spend on the party bags.

That means , Total cost ≤ $ 95

From (i)

7P  ≤  95   , which is the required inequality.

Explain why the graph of the quadratic function ()=2++5 crosses the y-axis by does not cross the x-axis

Answers

Answer:

The graph of a quadratic function is a parabola, and its parts provide valuable information about the function.

Step-by-step explanation:

A submarine dives below the surface, heading downward in four moves. If each move downward was 235
feet, where is the submarine after it is finished diving?
The submarine would be
feet below sea level, or
feet.

Answers

Answer:

Step-by-step explanation:

It drops 235 feet per move.

235 * 4 = 1140 feet below sea level.

-1140 is also possible.

The ratio of adult cats to kittens at a pet care center on was 5:2 . There were 12 kittens there that day. Thursday ​, 38 adult cats were at the pet care center. What is the difference between the number of adult cats at the pet care center on thursday and monday?

Answers

Answer:

8 adult cats

Step-by-step explanation:

The ratio of adult cats to kitten at the pet care center was 5:2

No of adult cats= 5x

No of kitten cats= 2x

Since there were 12 kittens that day

2x= 12

x= 12/2

x= 6

Number of adult cats = 5x

= 5 × 6

= 30 adult cats

Therefore since there were 38 adult cats in the pet center in Thursday then the difference between the number of adult cats in Thursday and Monday can be calculated as follows

= 38-30

= 8 adult cats

please help im struggling really bad on this one question.

Answers

Answer:

B

Step-by-step explanation:

90 degrees means 1/4 of 360 degrees. If you think about it like a clock it would be at 3:00. B is the representation of that

Answer:

B

Is going clock wise I dont really know how to explain it

How do I solve |x-1|-1.4 = 6.2

Answers

Answer:

x1= -6.6   x2= 8.6

Step-by-step explanation:

Answer:

x1= -6.6, x2= 8.6

Step-by-step explanation:

|x-1|-1.4=6.2

|x-1|=6.2+1.4

|x-1|= 7.6

x-1=7.6 or x-1= -7.6

x= 8.6 and x= -6.6

The value of -4 - x is positive. What must be true about x ?
i need help with this asap

Answers

Answer:

x must be less than -4

Step-by-step explanation:

We need to set the equation equal to 0

-4 - x > 0

+ -4   +   -4

x < - 4

The stemplot shows the number of magazines sold by students in a band. One data value was inadvertently omitted from the stemplot. A stemplot titled magazines sold has values 8, 9, 12, 12, 13, 15, 16, 16, 16, 18, 21, 22, 23, 27, 28, 32, 34, 40. Which statement is true? If the missing data value was 55, the range of the data would change significantly. If the missing data value was 55, the interquartile range of the data would change significantly. If the missing data value was 22, the range of the data would change significantly. If the missing data value was 22, the interquartile range of the data would change significantly.

Answers

Answer:

If the missing data value was 55, the range of the data would change significantly

If the missing data value was 22, the interquartile range of the data would change significantly

Step-by-step explanation:

Given the data

8, 9, 12, 12, 13, 15, 16, 16, 16, 18, 21, 22, 23, 27, 28, 32, 34,40

The range of the data is the difference between the highest value and the lowest value of the data.

Highest value = 40

Lowest value = 8

Range = 40-8

Range = 32

If 55 was missing, we need yo find the range of the data if 55 was included.

Highest value will be 55

Lowest value = 8

Range in this case = 55-8

Range = 47

Difference in range = 47-32= 15

This means that if 55 was missing, it will significantly affect the value of the range.

- Interquartile range = Q3-Q1

Q3 is the median value of the other half of the data.

Q1 is the median value of the first half of the data.

If 55 wasn't included, the first part of the data:

8, 9, 12, 12), 13, (15, 16, 16, 16

Q1 = 13 (median value of the extracted data)

The second part of the data if 55 wasn't included:

18, 21, 22, 23), 27, (28, 32, 34, 40

Q3 = 27 (median value of the second part of the data)

IQR = Q3-Q1

IQR = 27-13

IQR = 14

If 55 was included, the data will be;

8, 9, 12, 12, 13, 15, 16, 16, 16, 18, 21, 22, 23, 27, 28, 32, 34, 40,55

Q1 = N+1/4 the value

N is the sample size = 19

Q1 = 19+1/4

Q1 = 20/4

Q1 = 5th value

The 5th value in the data is 13, hence Q1 is 13

Q3 = 3(N+1)/4th value

Q3 = 3(19+1)/4

Q3 = 60/4

Q3 is the 15th value in the dataset. Since the 15th value is 28, Q3 is 28

IQR = 28-13

IQR = 15 (if 55 was included)

Difference in IQR = 15-14 = 1

This means that if 55 was the missing data, the IQR will not change significantly.

Note that the range of the data will not change if the missing value is 22 because, the 22 is a value lower than the highest value of the dataset, hence the range will remain the same (40-8 = 32) irrespective of 22 missing or not.

For the Interquartile range

If 22 was in

Q3 = 3(N+1)/4th value

Q3 = 3(19+1)/4

Q3 = 60/4

Q3 is the 15th value in the dataset. Since the 15th value is 28, Q3 is 28

IQR = 28-13

IQR = 15 (if 55 was included)

Difference in IQR = 15-14 = 1

This means that if 55 was the missing data, the IQR will not change significantly.

Based on the calculation, the correct options are:

- If the missing data value was 55, the range of the data would change significantly

- If the missing data value was 22, the interquartile range of the data would change significantly

Answer:

a

Step-by-step explanation:

edge 2021

please help, and it’s ok if you don’t understand it or get it wrong, please don’t feel guilty ^-^

Answers

Answer:

i think its 4.5

Step-by-step explanation:

Explain how Main Sequence Stars
are different from Giant stars and
Dwarf stars?


Help me with thissss

Answers

A giant star is a star with substantially larger radius and luminosity than a main-sequence (or dwarf) star of the same surface temperature. They lie above the main sequence (luminosity class V in the Yerkes spectral classification) on the Hertzsprung–Russell diagram and correspond to luminosity classes II and III.

Neptune is 2,798,842,000 miles from the sun. How many hours does it take lightto travel from the sun to Neptune?

Answers

9514 1404 393

Answer:

  4.17 hours

Step-by-step explanation:

The speed of light is about 670,616,629.4 miles per hour, so the travel time to Neptune is ...

  (2,798,842,000 mi)/(670,616,629.4 mi/h) ≈ 4.17 h

It takes about 4.17 hours for light to travel from the sun to Neptune.

Write the sentence as an equation.
m divided by 341 equals 315

Answers

Answer:

m/341=315

Step-by-step explanation:

Answer:

m/341=315 because the divided symbol is / and the equals symbol is = so replace the words with the symbol.

Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s). ∆ABC and ∆FDE are congruent by the criterion. (Use the three-letter abbreviation without spaces.) The value of x is , and the value of y is .

Answers

*See attachment for the given diagram.

Answer:

∆ABC and ∆FDE are congruent by the SSS criterion.

The value of x is 11 and the value of y is 8

Step-by-step explanation:

Based on the Side-Side-Side (SSS) Congruence Theorem, ∆ABC and ∆FDE are congruent to each other. The 3 sides of ∆ABC are congruent to the 3 given sides of ∆FDE.

Thus:

AB ≅ DF

BC ≅ DE

CA ≅ FE

Find x:

Since BC ≅ DE, therefore measure of BC = measure of DE.

BC = x + 3

DE = 14

Thus,

x + 3 = 14

Subtract 3 from each side

x = 14 - 3

x = 11

Find y:

Since AB ≅ DF, therefore the measure of both sides are equal.

AB = 3

DF = x - y

Thus,

x - y = 3

Substitute x = 11 into the equation

11 - y = 3

Subtract 11 from both sides

-y = 3 - 11

-y = -8

Divide both sides by -1

y = -8/-1

y = 8

Answer:

Below

Step-by-step explanation:

got it right

Geometry Question: Image is provided below.

Please show all work and your steps.

25 points

Answers

We know that the angle above 10x + 54 must be 8x because of Alternate angles. And we also know that angles in a straight line add up to 180. So we can infer that 10x + 54 + 8x = 180
We can simplify that into 18x + 54 = 180
Now we take away 54 from both sides to get 18x = 126
Now divide both sides by 18 and we get
x = 7.
Now that we know that x = 7 we know that the 10x + 54 angle is equal to 124 by substituting the value of x in. We also know that 11y + 14 must equal to 124 because of vertically opposite angles. So we have 11y + 14 = 124.

Take away 14 from both sides; 11y = 110
Now divide both sides by 11 and we get
y = 10

So x = 7 and y = 10
I hope that you understood all of my steps and if this did help you a Brainliest would be very appreciated :)

Answer:

x=7

y=10

Step-by-step explanation:

8x and 11y+14 are same side interior angles so they add to 180 degrees

11y+14 and 10x+54 are vertical angles so they are equal

8x + 11y+14 = 180

11y+ 14 = 10x+54

Substitute 10x+54 for 11y+14 in the first equation

8x +10x+54 = 180

Combine like terms

18x+54 =180

Subtract 54

18x+54-54=180-54

18x =126

Divide by 18

18x/18 = 126/18

x=7

Now we can find  y

11y+ 14 = 10x+54

11y + 14 = 10*7+54

11y+14 = 70+54

11y+14 =124

Subtract 14 from each side

11y = 124-14

11y =110

Divide by 11

11y/11=110/11

y =10

Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawals or deposits since then. If her interest rate is 8% each year, how much interest has accrued using simple interest?
Total Interest = $


What is Tarah's new total balance?

New Balance Total = $

Answers

Answer:  

Total interest = $28.72

New balance = $ 387.72

Explanation: Tarah has $359 in the bank. To find the amount of interest, multiply 359 by .08.

She gets $28.72 interest annually.

In one year, she will make $387.72.  (Add the total interest to her original balance)

Plz mark brainliest:)

Your free ride to work ends in 14 days. So, maybe you need a car? How much can you afford to spend? Below is what's available at a dealership near you. Which car should you buy? Before you decide, think about this: You do not have enough money in your account to buy a car. You'll have to finance your purchase. You'll have to put down 25% of the vehicle's selling price as a down payment.

Answers

Step-by-step explanation:

Kindly find attached a screenshot of the price list of some cars from motor 1 .com since you did not provide any in the question, and let us assume it is the same as what is available at a dealership near you.

From the list, since you don't have enough money in your account to buy a car, I will say you should get a 2017 Nissan Versa for $11,990

and 25% of  $11,990 is

(25/100)* 11,990

0.25* 11,990

$2997.5

So you can make a down payment of $2997.5

and pay the remainder of $8992.5 later

2. Express each of the following percentages as
a decimal.
(a) 4%
(b) 633%​

Answers

Answer:

a. 0.04

b. 6.33

Step-by-step explanation:

a. If we want to convert into decimal we need to divide it by 100 then answer will 0.04

4/100 = 0.04

b. If we want to convert into decimal we need to divide it by 100 then answer will 6.33

633/100 = 6.33

Pls help..it is an emergency...
Thank u

Answers

Answer:

Triangle A did a reflection over the x-axis and the translated down two units to become triangle B

Step-by-step explanation:

Hope this helps. Happy Halloween

help please !!!!! no explanation needed

Answers

It’s d I think I have to right to fill the character limit

Answer:

Its D super easyyyyyyh

I need help with this asap

Answers

Answer:

3\sqrt{3}

Step-by-step explanation:

look this up and it will give you the answer

pls mark brainliest

Answer:

The sqrt of 3 is an irrational number.

The sqrt of 9 is a rational number.

Step-by-step explanation:

hi, can someone please answer this?

Answers

Step-by-step explanation:

[tex] \frac{7}{27} [/tex]

it helps you ☺️☺️

Thank you ☺️☺️

HELP ME PLS one bottle of shampoo costs 6 dollars for 8 Oz a second bottle costs 4 dollars for 5oz of shampoo wich has a lower unit rate and how much lower

Answers

Answer:

The 8 oz has lower unit rate, it's lower by .2.

Step-by-step explanation:

8 oz divided by $6 = $1.333 for 1 oz  ---- (round to 1.3)

6 oz divided by $4 = $1.5 for 1 oz

A kayak is originally priced at $100. The online retailer gives a discount and the kayak is now priced at $75. Enter the percentage discount for the cost of the kayak.

Answers

Answer:

25%

Step-by-step explanation:

Discount:

  $100 * .25 = $25

New Price:

  $100 - $25 = $75

Helllpppp me please!

Answers

Answer:

b. 0.225

Step-by-step explanation:

tan = opposite / adjacent

opposite of A is 9

adjacent of A is 40

9/40=0.225

It is B 0.225 I don’t know for sure but I think it is

What is the volume of the cylinder below

Answers

Answer:

I think d or b

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

What does sin(-u) equal?
.
.
.
.
.
.
.
PLEASE HELP!!!

Answers

Answer:

-sin(u)

Step-by-step explanation:

This is a Trig identity.  The best way to understand this is to start at zero degrees.  +u would move counterclockwise, while -u moves clockwise.  The sine function gives you how far in the y-direction you are from the x-axis.  Since you're moving the same amount by going u degrees (or u radians) around the circle as you would going -u degrees (or -u radians), your distance from the x-axis is the same.  But it reflects over the x-axis, so the two outcomes are inverses of each other.

A local mechanic charges customers a flat fee of $60 before any work is done in the rate of 85 per hour for labor which equation represents the relationship between the total charge for labor L in dollars and the number of hours worked h?

Answers

Answer:

im not sure but here u go 85x+60

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