Question

Given: In ∆ABC, segment DE is parallel to segment AC .
Prove: BD over BA equals BE over BC

Answer 1

The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.




Statement

Reason


1. segment DE is parallel to segment AC

1. Given


2. Line segment BA is a transversal that intersects two parallel lines

2. Conclusion from Statement 1


3. ∡BDE ≅ ∡BAC

3. Corresponding Angles Postulate


4.

4.


5. ∆ABC ~ ∆DBE

5. Angle-Angle (AA) Similarity Postulate


6.

6.



Complete the proof by entering the correct statements and reasons.

Answer 2

what grade r u in? :3

Answer 3

9th

Answer 4

thats weird, I am in the same grade but I cant understand this >.> I dont think I went through this yet :(

Answer 5

Can u help me with a different question?

Answer 6

will try :)

Answer 7

@charlotte123 ????

Answer 8

@gocanes6 I will try :)

Answer 9

The pool should be a rectangular prism. Mrs. Noether wants the pool to hold between 1400 ft3 and 3200 ft3 of water and be from 6-10 feet deep. Other than those specifications, you are free to design the pool how you'd like!

The estimated cost of the pool, besides labor, will come from the pool lining material that coats the inside of the pool and the amount of water needed to fill the pool. Determine the following:
1.The dimensions for the Noether pool that fit the above specifications
2. The amount of pool liner material that will be needed to completely line the inside of the pool (sides and bottom)
3. The amount of water that will be needed to fill the pool if the water needs to be 6 inches below the top of the pool

*Please include the work involved in determining the above measurements or an explanation for how the measurements were determined.

Draft a proposal for the Noethers that includes the above information along with a drawing of their pool. You may need to create more than one drawing to correctly convey your idea.
My dimensions 8 ft deep, 4o ft wide, 5 ft long

Answer 10

@jim_thompson5910
@Mertsj
@mathslover

Answer 11

@BrandonGarza777

Answer 12

Angle BED = angle BCA

why is this true

Answer 13

corresponding angles postulate

Answer 14

good, that's what goes in line 4

Answer 15

the statement I provided and the reason you provided

Answer 16

Wait but that was already there for statement 3

Answer 17

statement 3 uses different angles, but it's similar

Answer 18

angle BDE is NOT the same as angle BED

Answer 19

Oh I didn't see that ok now next number 5

Answer 20

I mean 6

Answer 21

the last line is always what you want to prove

Answer 22

in this case, you want to prove that

BA/BD = BC/BE

Answer 23

why is that statement true

Answer 24

SSS postulate?

Answer 25

good, the converse of the SSS similarity postulate

Answer 26

Whats the converse of it?

Answer 27

the SSS similarity postulate states that if you have 3 pairs of sides proportional in a triangle, then the two triangles must be similar

the converse flips things around

Answer 28

the converse says that if you have 2 similar triangles, then the corresponding sides will be proportional

Answer 29

SO for the final ill put BA/BD = BC/BE and reason converse SSS postulate

Answer 30

converse of it

Answer 31

So BC/BE=BA/BD

Answer 32

Is that correct?

Answer 33

@jim_thompson5910 Is that correct?

Answer 34

that is correct, that's the statement for #6

Answer 35

OK now can u help me with my second question. Thank u for the first by the way:)

Answer 36

ok one sec

Answer 37

OK :)

Answer 38

so you made up a pool that is 8 ft deep, 40 ft wide and 5 ft long right?

Answer 39

yes now I need to find out the amount of pool liner material

Answer 40

ok all you have to do is find the surface area of the pool (think of it as a rectangular prism)

BUT

you are NOT counting the top surface because the lining doesn't apply there

Answer 41

So 2ab+2ac+2bc?

Answer 42

yes but remember you're subtracting off the top face

Answer 43

which is the surface of the water

Answer 44

So what would I remove from the formula?

Answer 45

well if a is your length and b is your width, then you change 2ab to ab

Answer 46

I actually don't have a calculator or a pen right now

Answer 47

ok then use google as a calculator

Answer 48

ex: if you typed in 2*3 + 8 into google, it will produce the result of 14

Answer 49

ok so I got 550

Answer 50

now what

Answer 51

@jim_thompson5910 now what sir?

Answer 52

one sec while I check

Answer 53

hmm I'm getting 920, how did you get 550?

Answer 54

I multiplied everything, and got rid of the 2's at the beginning like u said

Answer 55

like how u said 2ab, get rid of the two

Answer 56

8 ft deep, 40 ft wide, 5 ft long

D = 8
W = 40
L = 5


LW + 2LD + 2WD

5*40 + 2*5*8 + 2*40*8

200 + 80 + 640

920

So this shows that the total surface area of the liner is 920 square ft

Answer 57

OK so now that we have found the liner of the pool, we must fill the pool, like it says in the third part, how do we do this?

Answer 58

use the formula

volume = L*W*D

Answer 59

1600ft cubed

Answer 60

or cubic feet.
Theres another part of this problem, can u help me with it.

Answer 61

ok

Answer 62

The amount of water that will be needed to fill the pool if the water needs to be 6 inches below the top of the pool

so what you need to do is subtract 0.5 ft (6 inches = 0.5 ft) from the depth to get 8-0.5 = 7.5

this is your new depth, use it to calculate the new volume

Answer 63

After you present the plans to the Noethers, Mrs. Noether loves your drawing so much that she wants you to create a similar pool for the family dogs. She wants the dimensions of this pool to be one over four the dimensions of the family pool.

Determine the following:
1.The dimensions for the dog pool that fit the above specifications
2.The amount of pool liner material that will be needed to completely line the inside of the pool (sides and bottom)
3.The amount of water that will be needed to fill the pool if the water needs to be 6 inches below the top of the pool

*Please include the work involved in determining the above measurements or an explanation for how the measurements were determined.

Draft a proposal for the Noethers that includes the above information along with a drawing of their dogs' pool. You may need to create more than one drawing to correctly convey your idea.
Answer the following questions:
1.What relationship does the volume of the dogs' pool have with the volume of the original family pool? How does this compare to the relationship in the dimensions of the dogs' pool to the dimensions of the family pool?
2.What is the difference in volume when the pool is filled to the top versus filled to 6 inches below the top?
3.Was the amount of pool liner material representative of the lateral or surface area of a rectangular prism? Why or why not?
4.Imagine Mrs. Noether asked you to add steps to the family pool. How would adding steps affect the volume of the water? How would adding steps affect the amount of pool liner material needed? Explain why each change would take place.

Answer 64

you'll follow the same basic steps as we did before

but you'll make each dimension 1/4 of the original corresponding dimension

ex: 8 ft deep ---> 8/4 = 2 ft deep

so the dog pool is 2 ft deep

Answer 65

10 feet wide, but what about the length?

Answer 66

5/4 = 1.25 ft long

Answer 67

ok so le=iner is 50 ft

Answer 68

and the volume is 18.75 ft cubed.

Answer 69

now what about the questions?

Answer 70

What relationship does the volume of the dogs' pool have with the volume of the original family pool?

Answer 71

compare the two and tell me what you think

Answer 72

it is much less lol

Answer 73

what else

Answer 74

It is unable to hold as much water as the original. Also it is 30 times greater than the puppy pool

Answer 75

each dimension of the dog pool is ____ times smaller than the original pool

Answer 76

fill in that blank

Answer 77

a quarter smaller

Answer 78

so the smaller pool is (1/4)^3 = 1/64 times smaller in volume compared to the big pool

Answer 79

ie...

Small pool volume = (Large pool volume)/64

Answer 80

why 64?

Answer 81

because 4^3 = 64

Answer 82

if you doubled the dimensions, then the volume would be multiplied by 2^3 = 8

Answer 83

Ok so what would I put for the first question?

Answer 84

the first question is basically answered already

Answer 85

I put, The dog’s pool is much smaller, and holds much less than the human’s pool. In other words, if you divided the volume of the large pool by 64, it would equal the volume of the dog’s pool.

Answer 86

yep that's basically what they want

Answer 87

OK so next question

Answer 88

maybe some explanation how you got the 64 as well

Answer 89

2.What is the difference in volume when the pool is filled to the top versus filled to 6 inches below the top?

find the two volumes, then subtract

Answer 90

The difference between the volumes of the puppy pool with the added six inches is about 6 ¼ ft. For the human pool, the difference is 100 ft.
That's what I wrote

Answer 91

when talking about volume, your units will be in cubic feet

Answer 92

Ok next

Answer 93

so the diff for the dog pool is 6 1/4 cubic feet

the diff in the human pool is 100 cubic ft

Answer 94

Was the amount of pool liner material representative of the lateral or surface area of a rectangular prism? Why or why not?

you tell me

Answer 95

yeah what about the next question

Answer 96

any ideas?