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#1 2015-11-07 14:26:36

Lpravia020614
Member
Registered: 2015-11-03
Posts: 35

Proofs !

Someone please help! I am stuck on proofs!


State whether the following are given, unfounded or covered by a particular definition.  Provide the explanation for your selection:

1. If I have two coplanar lines, I must have a plane.

2. There are two adjacent angles whose outside edges form a straight line. The measure of the first angle is 100 degrees, so the measure of the other must be 80 degrees

3. I have drawn a polygon with eight sides, so it must be an octagon.

4. A square has two diagonals.

5. If the diameter of the circle is 12, the radius must be 6.

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#2 2015-11-07 15:26:07

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Proofs !

hi Lpravia020614

Q1.  I ask myself whether I can think of a case where this doesn't result in a plane.  Even if the lines are parallel, there's still a plane so I can dismiss 'unfounded'.  The plane conclusion isn't stated so I guess you are meant to say 'covered by a definition'.

Q2.  Isn't this also covered by the definition that the angles of a straight line add up to 180 ?

Q3.  This also sounds like the definition of an octagon.

Q4.  Since a square has four vertices and a diagonal joins opposite vertices this seems to follow from these definitions.

Q5. And this from the definitions of diameter and radius.

So when will a question be 'given'?  I'd like to see an example.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2015-11-07 15:28:47

Lpravia020614
Member
Registered: 2015-11-03
Posts: 35

Re: Proofs !

I don't really understand I have two lesson left in my online course and then I'm done but the way they format the problems make them Confusing. I can't access the questions right now to show all of them, I think there's 20 questions in total so I'll get back to you tomorrow.

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#4 2015-11-07 15:31:31

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Proofs !

OK.  It's the middle of the night in the UK.  I just happened to be awake. sleep.  I'll check again in the morning.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#5 2015-11-07 15:32:31

Lpravia020614
Member
Registered: 2015-11-03
Posts: 35

Re: Proofs !

It's 10:30 here. Just email me when you get the chance and ill most likely be awake. Doesn't matter what time.

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#6 2015-11-07 15:40:48

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Proofs !

I'm waiting to see Q6 - Q20.

Back to bed now.  sleep

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#7 2015-11-07 15:42:55

Lpravia020614
Member
Registered: 2015-11-03
Posts: 35

Re: Proofs !

Use the following images for questions 6 through 10:

6. In the figure above, line segment MC is equal to imaginary line segment MI.

7. In the figure above, line segment EJ is equal to line segment JM.

8. In the figure above, the measure of angle AMC is 90 degrees.

9. In the figure above, the measure of arc AC is 90 degrees

10. In the figure above the measure of angle AME is x degrees, then the measure of angle EMB is 180-x degrees.

11. In a right triangle where one side is 3, and the hypotenuse is 5, the remaining side must be 4.

12. In a triangle, if I have two angles that add up to 50 degrees, the remaining angle must be 130 degrees.

13. The diameter of a circle always passes through the midpoint of the circle.

14. If a central angle is 30 degrees, then the arc it defines is also 30 degrees.

15. The area of a sphere is 4 times the area of a circle with the same radius.

16. If a radius bisects a chord, then the lengths of the parts of the radius on either side of the chord are equal.

17. If a circle has a central point M, and both point A and point D are on the circle, then ls_MA and ls_MD will be equal.

18. If I have two points, (-2, -3) and (-4, 4) then the distance between them is sqrt(53).

19. The given points (4, -8), (4, -5), and (-2, -6) make a right triangle.

20. The given points (2, -3), (-7, -7), (2, -7), and (-7, -2) make a square.

There's a picture to go along with this. I don't know if it posted. Will have to get on the laptop tomorrow. Goodnight.

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#8 2015-11-07 20:45:28

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Proofs !

hi

I hate these questions. I'm not surprised you have asked for help.  Why do CompuHigh do this ?  None of these questions contains a proof, because they don't actually show how they came to any conclusion..  Do they understand what a proof is ?  Here's an example of a proof:

ABC is a triangle.  BC is extended to point D.

Angle ABC = 50 and angle BAC = 30.  Everything so far is given information.

Angle ACB = 180 - 50 - 30 = 100.  (angle sum of a triangle)
Angle ACD = 180 - 100 = 80.         (angles on a straight line)

These are deductions made from definitions.

Elephants have big ears. Although this is TRUE it has not been proved by what came before so it is unfounded.

End of example.

So a proof will always have some given information, followed by deductions made from definitions or earlier deductions.

All 20 questions have given information, so I am uncertain when you are supposed to make given your chosen answer.  I am going to assume that what they mean is 'say given when there is no following deduction or false conclusion'.

On that basis I have changed my mind about answer Q1.  AS you are told the lines are coplanar the following statement that we have a plane is not a deduction because we are merely repeating what we were told.  Similarly Q3 is just the statement without any proof so I'll change that to given too.

The other three (Q2, Q4 and Q5) can be proved from the given information so I'll say they are covered by a particular definition.

Now for the rest.

I have no diagram so cannot help with 6-10.  If you are having difficulty posting an image, you could try describing the diagram with sufficient detail that I can make my own diagram.

11. In a right triangle where one side is 3, and the hypotenuse is 5, the remaining side must be 4.
Check this out with Pythagoras.

12. In a triangle, if I have two angles that add up to 50 degrees, the remaining angle must be 130 degrees.
Check this out with angle sum of a triangle.

13. The diameter of a circle always passes through the midpoint of the circle.
14. If a central angle is 30 degrees, then the arc it defines is also 30 degrees.
I think these are just statements rather than proofs. EDIT I read this as angle at the edge.  Happy3690 has it right in the next post.

15. The area of a sphere is 4 times the area of a circle with the same radius.
Check this out by comparing the formulas.

16. If a radius bisects a chord, then the lengths of the parts of the radius on either side of the chord are equal.
You have to prove this using congruent triangles.

17. If a circle has a central point M, and both point A and point D are on the circle, then ls_MA and ls_MD will be equal.
this looks like a statement or definition of the concept of a radius/circle.

18. If I have two points, (-2, -3) and (-4, 4) then the distance between them is sqrt(53).
Check this out with Pythagoras.

19. The given points (4, -8), (4, -5), and (-2, -6) make a right triangle.
Check this out with Pythagoras. Alternatively you could calculate gradients.  If one line has gradient m1 and the second has gradient m2, m1.m2= -1 if and only if the lines are perpendicular.

20. The given points (2, -3), (-7, -7), (2, -7), and (-7, -2) make a square.
This could be proved by checking the lengths by Pythagoras and the gradients as above.

Sorry I cannot be more positive.  Note to other readers:  If you are wondering whether to enrol with CompuHigh, I have some useful advice.  Make a new post "Would you recommend I enrol on the CompuHigh math course" and I'll tell you what I think.  smile

Bob

Last edited by Bob (2015-11-07 23:25:17)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#9 2015-11-07 21:21:07

Happy3690
Member
Registered: 2015-11-07
Posts: 2

Re: Proofs !

I can't see the figure you are talking about so I don't know about 6 to 10.

11. Pythagorean theorem states that if a triangle us right angled it's a^2+b^2=c^2 where the hypotenuse is c and the shorter sides are a and b. So if the hypotenuse is 5 and one of the sides are 3 we get, 3^2+b^2=5^2.therefore b is 4 and the statement is true.



13.It always does.The statement is true.

12.Angles in a triangle add up to 180 so the last angle is 180-50 or 130 degrees.So the statement is true.

14.The statement is wrong the angle at the edge of a circle are double that of the circumference.So the arc it defines is 60 degrees.

15.The formula for the area of a circle is pir^2 and the surface area of a sphere is 4pir^2.So the statement is true

16.The statement is true

17.Yes because the distance from the midpoint to a point on a circle is always the same.

18.Yes because -4--2=-2 and 4--3=7 and pythagorean theorem states that a^2+b^2=c^2 so 49+4= c^2 or c =sqrt(53).

19.No because
For it to be a right angled triangle the point that is on a different point on the x/y axis has to have one common coordinate.Which it dosen't.

20.No because some of the points are 4 away from eachother where as others are 9 away.

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#10 2015-11-08 00:13:58

Lpravia020614
Member
Registered: 2015-11-03
Posts: 35

Re: Proofs !

Thank you! I don't see why they make it harder than what it really is! This really helped me !

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