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**demha****Member**- Registered: 2012-11-25
- Posts: 186

This is my final test. If you help me with this, then you have officially helped me finish geometry! I will be posting 5 at a time. In this lesson, there are quite a few pictures or math symbols i am not sure how to make. So I just took an image of the page with the first 5 questions and will post it here to view.

#1 - my answer is 'B'

#2 - my answer is 'B'

#3 - *need help understanding how to solve

#4 - i think 'A' would be the answer

#5 'D'

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

Hi;

1)do not agree.

2) agree

3) I like C. ( Just a little algebra )

4) do not agree.

5) agree

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

#1 - how would I do this? I thought complimentary angles added up to 90 degrees and so that is why I chose 'B', 55 degrees.

#3 - so C is the answer, but in the future if I ever come across anything like this, how would I do the work to get my answer?

#4 - would prefer help understanding how to solve this.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

Hi;

1)

The smaller angle is 35 degrees less. Call the smaller angle x. So

x + (x + 35 ) = 90

2x + 35 = 90

2x = 55

x = 27.5 so the larger angle is 27.5 + 35 = 62.5

4) Those are not vertical angles so they are not equal so A and D are out.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

#1 - I see now, I just had the two final steps (diving by two then adding to 35) missing from my calculations. So the true answers will be 'C'

#4 - i'm not sure exactly what I would be searching to find out more about this problem. What would this be called?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

HI;

Angle A = Angle D and Angle B = Angle C

Angle A and Angle C are supplementary, So B and D are supplementary. Since B = C and A and C are supplementary then B and A are supplementary.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

#4 - so answer is 'C'! Now if the angles were on the opposite side, would it be considered complementary?

As we go through that, here are the next 5:

#6 - answer 'C'

#7 - answer 'C' (lots of answers being 'C' so far!)

#8 - i go with 'A'

#9 - 'B'

#10 - **not sure how I would get the measusements for that. i know that the top triangle has sides of 16 - 16 - 8. The shape on the bottom has a base of 14 and if you would say a "top" of 8.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

Complementary angles are angles that sum up to 90 degrees.

Before we move on did you get #3? It requires a little algebra.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

No I haven't. I was hoping you would help explain to me then we can start on the next 5.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,443

#3

There may be an easier solution but this is how I did it.

Call x the total distance of the line. Give each line segment a name.

For instance AE is the distance from point A to point E.

Then from the drawing and what is given the following relationships hold.

AE = x

AC = CE

AC + CE = x

CD + DE = x/2

CD = DE

AB + BC = x/2

DE = 5

BC = 2

AB + BC + CD + DE = x

Using line 5,7 and 8 and substituting you can shorten that to,

AC + CE = x

10 = x/2

2 + AB =x/2

12 + AB = x

AC = CE

the second equation can be solved for x. We get x = 20. So 20 is the distance of the line segment AE.

Now we can solve directly for AB by using the 4th equation.

12 + AB = 20

AB = 8.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,383

hi demha and bobbym,

You can get AB in Q3 just by working the distances.

C is the midpoint of CE and D is the midpoint of CE.

DE = 5 => CE = 10 => AC = 10

BC = AC - BC = 10 - 2 = 8

Q10. Triangles KPN and KJQ are similar ( one common angle and the parallel lines)

So there is a scale factor that will enlarge a length in KPN into the corresponding length in KJQ.

We know that PN = 8 and JQ = 14 so the scale factor is

From this you can work out NQ.

Q8. The largest length in a triangle is opposite the largest angle; the middle sized length is opposite the middle angle and the smallest length is opposite the smallest angle. So use Pythag to work out BC first. Then you can put the sides in order of size and thus the angles in order of size.

Q6, Q7 and Q9 are correct

Bob

*Last edited by bob bundy (2013-09-28 19:45:40)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

#3 - I see now it makes MUCH more sense. AC and CE make up the entire line. D is the midpoint of CE. So if DE = 5, then CE = 10. And since AC = CE, AC also equals 10. We want to find out length of AB. So what we do is AC - BC which is 10 - 2 = 8!

---

#8 -

I go an answer of 6.32. Is that correct so far?

#10 - 16 x 14/8 = 28, which is 'A'

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,383

hi demha,

Q8. Yes, correct so far. So now you can sort out the smallest angle etc etc.

Q10 So KQ = 28. Tick. But that isn't what the question asks for. One more step needed.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

#8 - So 6.32 would be the answer for the third side correct? If so, would I be using the method shown on this webpage to find my angles:

http://www.mathsisfun.com/algebra/trig-solving-sss-triangles.html

#10 - I see it now! KQ is 28, KN is 16. They want NQ. So KQ - KN which is 28 - 16 = 12!

*Last edited by demha (2013-09-29 00:41:38)*

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,383

hi demha

#8 - So 6.32 would be the answer for the third side correct? If so, would I be using the method shown on this webpage to find my angles:

http://www.mathsisfun.com/algebra/trig-solving-sss-triangles.html

Too much. You don't have to find the measure of the angle. Just say which is bigger.

RULE FOR ANY TRIANGLE:

**largest side opposite largest angle**

**middle side opposite middle angle**

**smallest side opposite smallest angle**

You know the lengths of all the sides so you can put the angles in order of size and then choose an answer.

#10 - I see it now! KQ is 28, KN is 16. They want NQ. So KQ - KN which is 28 - 16 = 12!

Correct!

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

So measure B is greater than measure A.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,383

Hi

That's correct.

Bob

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Alright.Here is the next :

#11 - I go with 'D'

#12 - 'C'

#13 - 'C'

#14 - 'A'

#15 - 'C'

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi demha

Q11 is incorrect. All your other answers are correct.

Do you know what a statement's contrapositive is?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Not entirely. Could you explain?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,383

hi demha,

If it wags its tail then it's a dog. Contrapositive: If it's not a dog then it doesn't wag it's tail.

P => Q Contrapositive: NOT Q => not P

Any statement and its contrapositive express the same logic.

Look at the diagram. If P is totally contained in Q and we have a member of P, then we can be sure it is also a member of Q

If we know something is NOT a member of Q, then it cannot be a member of P.

If P is the set of tail wagging creatures and P is totally contained in Q, the set of dogs, then we know that wagging creatures are all dogs.

If we find a creature that is not a dog, we can be sure it doesn't wag its tail.

Note: The statement doesn't have to be true to be able to construct its contrapositive.

Bob

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

It's starting to make more sense. I'm looking between 'B' and 'C' but, I think I will go with 'B'.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

B is correct, because besides negating both sides, you need to switch them. From P⇒Q you get NOT Q⇒NOT P.

It is kinda logical when you try it out for different things. E.g. for P=I am less than 30 years old and Q=I am less than 90 years old, we can form the true statement: "If P is true then Q is true", that is "If I am less than 20, then I am less than 90 years old".

Now, if you want to find the contrapositive of that you would get "If Q is not true, then P is not true", which translates to plain English as "If I am more than 90 years old, then I am more than 20 years old", which is kinda logical, right?

I tried to explain it as best as I can, so sorry if it confuses you!

*Last edited by anonimnystefy (2013-09-30 08:49:33)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Little confusing, but I'm understanding it more. Thanks!

Here are the final 5 Geometry problems:

[img]ttp://imageshack.us/a/img845/3231/ht1p.png[/img]

#16 - 'A'

#17 - They want me to round it up to the nearest whole number. The radius is 6.5. Am I supposed to go upward to get answer 'C' - 8 OR downwards to get answer 'B' - 5?

#18 - **need help how to solve

#19 - 'C'

#20 - **not entirely sure how to solve this one.

*Last edited by demha (2013-10-01 06:25:30)*

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Not sure why the above picture hasn't appeared, but here is another hopefully it will work:

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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