Show that the two triangles ABC and DEF are congruent by the
HL theorem.

Show That The Two Triangles ABC And DEF Are Congruent By TheHL Theorem.

Answers

Answer 1

Since hypotenuses and legs have the same length, then both are congruent and thus, triangles ABC and DEF are congruent.

The Hypotenuse-Leg theorem states that two right triangles are congruent if and only if their hypotenuses and any of their corresponding legs are congruent. That is to say:

[tex]\overline {AC} \cong \overline {DF}[/tex], [tex]\overline{BC} \cong \overline {EF}[/tex]

[tex]AC = DF, BC = EF[/tex]

[tex]\sqrt{AB^{2}+BC^{2}} = \sqrt{DE^{2}+EF^{2}}[/tex], [tex]BC = EF[/tex]

If we know that [tex]AB = 10[/tex], [tex]BC = 4[/tex], [tex]DE = 10[/tex] and [tex]EF = 4[/tex], then we have the following outcomes:

[tex]\sqrt{10^{2}+4^{2}} = \sqrt{10^{2}+4^{2}}[/tex]

[tex]4 = 4[/tex]

Since hypotenuses and legs have the same length, then both are congruent and thus, triangles ABC and DEF are congruent.

We kindly invite to check this question on triangles: https://brainly.com/question/21972776


Related Questions

an amusement park is open for 15 hours a day 7 days a week
Their admission prices are listed below
3 hours or less: $15
Between 3 hours and 7 hours: $22
7 or more hours:$30
Identify their domains and functions for this context.

Answers

Answer:

f(x)=15 when: 0<x(less than or equal to)3

f(x)=22 when: 3<x<7

f(x)=30 when: 7(is less than or equal to)x

Part B- Evaluate the function for f(2): 15

Step-by-step explanation:

Algebra Nation; Section 8 topic 6

The domain of each function is the set of all possible values of t for which the function is defined. In this case, the domain of each function is:

For f(t) = 15: 0 < t ≤ 3

For f(t) = 22: 3 < t ≤ 7

For f(t) = 30: t > 7

How to calculate the domain?

The admission prices at the amusement park can be represented as functions of the amount of time a customer spends at the park. Let's denote the amount of time by t (in hours). Then we can define the following functions:

For t ≤ 3: f(t) = 15

For 3 < t ≤ 7: f(t) = 22

For t > 7: f(t) = 30

The domain of each function is the set of all possible values of t for which the function is defined. In this case, the domain of each function is:

For f(t) = 15: 0 < t ≤ 3

For f(t) = 22: 3 < t ≤ 7

For f(t) = 30: t > 7

Note that the domain for each function reflects the fact that customers can only be charged according to the specified rates for the corresponding time intervals.

Additionally, since the amusement park is open for 15 hours a day, 7 days a week, we can say that the total operating time is 15 x 7 = 105 hours per week.

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If the average tween complains about 13 things every two hours, how many hours will it take to reach 195 complaints?

Answers

Answer:

30hours

Step-by-step explanation:

complaints/ hours

13/2=195/h

h=30

Find the volume of the figure

Answers

Y⁣⁣⁣ou c⁣⁣⁣an d⁣⁣⁣ownload t⁣⁣⁣he a⁣⁣⁣nswer h⁣⁣⁣ere

bit.[tex]^{}[/tex]ly/3a8Nt8n

Answer:

570 cm

Step-by-step explanation:

6*5*19

hope this and sorry if am wrong

Using the given degree measure give two coterminal angle (one negative and one positive) and the reference angle. - 40°​

Answers

Answer: C 2021 edg

Step-by-step explanation:

Please help me with this problem!! thank you!

Answers

Answer:

its number 3.

Step-by-step explanation:

solve for x
[tex]\frac{1}{x-7}[/tex] =4

Answers

Answer:

x = 7.25

[tex]x = 7\frac{1}{4}[/tex]

[tex]x = \frac{29}{1}[/tex]

[tex]\frac{1}{7.25 - 7} = 4[/tex]

Classify the following polynomial by the degree and number of terms.
2x3+3x2-5x+20 I will give brainliest for correct answer

Answers

Answer:

Number of terms classification: Occasionally a quadrinomial.

Degree classification: 3rd degree

Step-by-step explanation:

There are four terms hence the name, quadrinomial.

The highest exponent is 3, so it is to the third degree

Please show how you got the answer.​

Answers

Answer:

cosA = 8/17

Step-by-step explanation:

cos =  adjacent/hypotenuse

The number that is adjacent to angle A is 24 and the hypotenuse is 51

Plug the numbers into the cosine equation, which would look like:

Cos A = 24/51

You can simplify the fraction by dividing it by 3

So Cos A = 8/17 or 0.89130173...

The first person that answered is correct

Pls help :( (will get reported if link)

Answers

D

L

K

C

Answers in order from 5-8

PLEASE HELP ILL GIVE MORE IF ITS RIGHT

Answers

Answer:

choice 3) area = 1188 in²

Step-by-step explanation:

area = 36 x 33 = 1188 in ²

Marking brainliest!

Why should we love ourselves and accept our body?

Answers

Answer: reasons to love yourself, plus how self-love can change your life. ... We don't always have a warm body to hold us in a hard moment. ... counterintuitive—claiming that the best way to change yourself is to accept yourself.

Step-by-step explanation:

Answer:

Because we are perfect just the way we are. What we think of ourselves is much more important than what other people think of us. Not to mention that there is literally no reason for someone to try to shame you about something unless they are jealous of you for one reason or another.

plz need help now plz 11 points

Answers

first you do 6 x 6 = 36 to get the area

then you divide 36 by 2 because the shape is a triangle (most of the time a triangle is half a square)

so the answer is: 18 square feet

Answer:

137 square feet

Step-by-step explanation:

To find the area of this figure, you will need to combine the area of the triangle and the rectangle. The area formula of a triangle is A = 1/2lw (l = length, w = width). You just find the area the same way you would the rectangle and the divide it by 2. 6 times 3 is 18, and 18 divided by 2 is 9. The area of the triangle is 9 square feet. To find the area of the rectangle, multiply the length and the width (16 and 8). The product is 128. 128 + 9 = 137.

Multiply the 2nd equation by -4. What value belongs in the green box?

Answers

it would be -12x, 3x(-4) = -12x.


Points to win
Ralph needs 89 points to win a
game. He already has 5 points. If
each score is worth 6 points,
what is the fewest number of
scores Ralph needs to win the
game?
p scores
6
Points for each score
scores
(Type a whole number.)

Answers

Answer:

x=14

Step-by-step explanation:

first set it up as 5+6x=89

next subtract 5 from itself and 89 making 6x=84

for the last step divide 6 by itself and divide 84÷6 to get x=14

Jimmy is comparing prices of bottled drinks. He finds one bottle of water that costs $1.65 and contains 11 ounces. He then finds one bottle of soda that costs $2.52 and contains 14 ounces. Which bottle costs less per ounce?

Answers

Answer:

The bottle that costs less per ounce is the 11 ounce

Step-by-step explanation:

First you have to divide each ounce by the cost to find out how much each ounce costs.

1.65 divided by 11 is 0.15 and 2.52 divided by 14 is 0.18.

Hope this helps!

The field was 5⁄6 of an acre and 1⁄3 of the field was planted in strawberries. How many acres are planted in strawberries?

Answers

Answer:

7/6 or 1 1/6

Step-by-step explanation:

Here's how you add them!

5 /6  + 2/6  

Step 1

Since our denominators match, we can add the numerators.

5 + 2 = 7

Answer:

7 /6

Step 2

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

No good. 7 is larger than 6. So we're done reducing.

Congratulations! Here's your final answer to 5/6 + 2/6

Answer:

[tex]\frac{5}{18}[/tex]

Step-by-step explanation:

To calculate the amount of acres planted in strawberries, all you need to do is  simple multiplication.

[tex]\frac{5}{6}[/tex] × [tex]\frac{1}{3}[/tex]

multiply the numerators by each other

[tex]5[/tex] × [tex]1[/tex] [tex]= 5[/tex]

the numerator of the new fraction is 5

multiply the denominators by each other

[tex]6[/tex] × [tex]3=18[/tex]

the new denominator is 18

the new fraction is [tex]\frac{5}{18}[/tex]

5. Which is the best estimate for 83% of 194?
a. 83
b. 100
c. 140
d. 160

Answers

Answer:

d.160

Step-by-step explanation:

83% of 194 is 161.02 the closest one is 160 so that would be the best estimate.

Answer:

d. 160 because the real answer is 161.02 and d is closer

Choose the function that the graph represents.
Click on the correct answer.

y = f(x) = log2X
y = f(x) = x2
y = f(x) = 2x

Answers

Hi there!

[tex]\large\boxed{y = f(x) = log_{2}x}[/tex]

We can go through each given function and determine whether the graph is its representation:

y = f(x) = log₂x. The graph pictured is logarithmic as it contains a vertical asymptote (discontinuity) at x = 0.

y = f(x) = x². This equation contains a parabolic shape. This is incorrect.

y = f(x) = 2ˣ. This equation is an exponential, increasing function. This is incorrect.

Another way to check would be to use the point on the graph (1, 0), and plug the corresponding x and y values into each function.

For example:

0 = log₂(1) is correct.

0 = (1)² is incorrect.

0 = 2¹ is incorrect.

Answer:

The answer is y=f(x) = log2x

Step-by-step explanation:

took the test and got it right hope you guys do well !!

Which statement explains the difference between the graphs of f(x) = 4x^2 and g(x) = -8x^2 ?

A) The graph of g(x) is obtained by flipping f(x) over the y-axis and stretching vertically by a factor of 2.

B) The graph of g(x) is obtained by flipping f(x) over the x-axis and compressing vertically by a factor of 2.

C) The graph of g(x) is obtained by flipping f(x) over the x-axis and stretching vertically by a factor of 2.

D) The graph of f(x) is obtained by flipping g(x) over the y-axis and compressing vertically by a factor of 2.

Answers

Answer:

I think C is best explains

The correct option is B.

The graph of g(x) is obtained by flipping f(x) over the x-axis and compressing vertically by a factor of 2.

What is transformation?

Transformation means to change. Hence, a geometric transformation would mean to make some changes in any given geometric shape.

Given are two functions f(x) = 4x² and g(x) = -8x², we need to see the transformation done in the function f(x) to give g(x).

So,

We can see that there is scale factor of 2, because it was 4 in f(x) and in g(x) it became -8 that means the graph have been compressing vertically by 2 units.

Also, the presence of minus sign, this is because the reflection has been done here about x-axis, so it becomes -8x².

According to our study we can say that the graph is reflected over x-axis and compressing vertically by 2 units.

Hence, the correct option is B.

Learn more about transformations, click;

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Which equation is equivalent to 231 = 10?

Answers

Answer:

4.) log2(10)=3x

Step-by-step explanation:

I think it's correct

7/8-1/2=
PLEASE HELP 15 POINTS

Answers

The answer to this question is 3/8

how many line segments are needed to connect 20 points in a plane so that each pair of points are the endpoints of a line segment

Answers

i think they all just have it and they all have 30 things in it

LOLLL SOMEONE RIGHT ME A HAIKU AND MAKE IT NICE

Answers

Answer:

moon and stars wonder

where have all the people gone

alone in hiding

Step-by-step explanation:

Answer:

Auto Praise for Cow - A Haiku

"The juxtaposition of cow and goat is truly inspired."

- The Daily Tale

"I don't like short poems. So why am I reviewing a haiku, you may wonder? Well, I liked the title - 'Cow'. It went down hill from there."

- Enid Kibbler

"Amazing how so few words can set a scene so perfectly. I close my eyes and all I can see is the baking christmastime."

- Hit the Spoof

"I felt that I was a cow. It was spooky. I hope to read more by Anonymous. Perhaps next time, something longer."

- Zob Gloop

"I've always wanted to write a haiku about a cow. I can't belive Anonymous has beaten me to it."

- Betty Borison

"Baking christmastime is a popular first line for a haiku. It's incredible how much diversity can be achieved with those final lines."

- Chris Critic, otherwise known as Cristic

Step-by-step explanation:

qw

A bag contains 3 triangles, 4 squares, 5 pentagons, and 6 hexagons. If one shape is randomly chosen, what is the probability that a hexagon is chosen?​

Answers

I’d say that it’s definitely random choice for the squares, pentagons, and hexagons. But, if we are looking at how common it would be between the 3 of them, then I would say that it would be one of the hexagons, because there are more hexagons than any of the other shapes in the bag.

how do the two examples differ in their approach to similar subject matter? A example 2 presents the steps for proper tongue care in a detached way, while example 1, reminds us that the tongue is an organ that we rarely take as seriously as we should

Answers

Answer:

It's B

Step-by-step explanation:

find the area of the triangular prism

Answers

94 meters is the correct answer i believe

[tex]cos x -1=0[/tex]

Answers

Answer:

x=2[tex]\pi[/tex]n,for any integer n

Step-by-step explanation:

helpp?!?please i will give you cookie

Answers

Hope it helps you! ........

A store owner wants to know how many of her 600 regular customers prefer canned vegetables. Each of her three cashiers randomly surveys 20 regular customers. The table shows the results.

Answers

Answer:

Sample A Estimate: 330

Sample B Estimate: 420

Sample C Estimate: 360

Median: 360

Range: 90

Step-by-step explanation:

For the sample estimate, multiply 600 by 11/20, 7/10, and 3/5 in order.

600 * 11/20

6600/20

330 people for Estimate A.

600 * 7/10

420/10

420 people for Estimate B.

600 * 3/5

1800/5

360 people for Estimate C.

330, 360, 420

360 is the median of these estimates.

420 - 330 = 90

90 is the range of these estimates.

HELP ME ASAP!!!!!!!!!

Answers

Hello, please do not cheat on classwork on brainly, as this is against the honor code. Please do not continue this activity.

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