2012 Year 9 &10 Mathematics Marathon (4 Viewers)

[Fawun]

Re: 2012 Year 9 &10 Mathematics Marathon

I don't know how to find the area of the white curved bits next to the petals to subtract it from my rectangle

 

[enoilgam]

Re: 2012 Year 9 &10 Mathematics Marathon

I don't know how to find the area of the white curved bits next to the petals to subtract it from my rectangle

Square! Well, what I did (again, I dont know if this is the best method), was divide the square into four parts. Maybe that helps.

 

[SpiralFlex]

Re: 2012 Year 9 &10 Mathematics Marathon

Okay here is a nice question with a nice solution if anyone is able to come up with an elegant way of prove. I think it is suitable for Year 9-10 level.

This is in fact Euclid’s fifth proposition in the first book of his Elements (Base angles in an isosceles triangle are equal)

 

[deswa1]

Re: 2012 Year 9 &10 Mathematics Marathon

@Fawun- small hint. There's more than one circle in the picture- there's the one that has its centre in the square in the middle and four quarter circles from the outside if that makes sense.

 

[kazemagic]

Re: 2012 Year 9 &10 Mathematics Marathon

Okay here is a nice question with a nice solution if anyone is able to come up with an elegant way of prove. I think it is suitable for Year 9-10 level.

This is in fact Euclid’s fifth proposition in the first book of his Elements (Base angles in an isosceles triangle are equal)

lol wut congruent triangles

 

[SpiralFlex]

Re: 2012 Year 9 &10 Mathematics Marathon

lol wut congruent triangles

Elaborate.

 

[kev-]

Re: 2012 Year 9 &10 Mathematics Marathon

yay I got it . For me the hardest step was actually visualising the actual shape.. won't give anymore away even though that was pretty vague

 

[kazemagic]

Re: 2012 Year 9 &10 Mathematics Marathon

Elaborate.

draw a perpendicular line

 

[Fawun]

Re: 2012 Year 9 &10 Mathematics Marathon

Okay here is a nice question with a nice solution if anyone is able to come up with an elegant way of prove. I think it is suitable for Year 9-10 level.

This is in fact Euclid’s fifth proposition in the first book of his Elements (Base angles in an isosceles triangle are equal)

AB = AC (given)

Angle ACB = Angle ABC (base angles of an isosceles triangle are equal).

Now back to enoilgams question.

 

[SpiralFlex]

Re: 2012 Year 9 &10 Mathematics Marathon

draw a perpendicular line

More info. I want an more elegant way, keep thinking.

 

[SpiralFlex]

Re: 2012 Year 9 &10 Mathematics Marathon

AB = AC (given)

Angle ACB = Angle ABC (base angles of an isosceles triangle are equal).

Now back to enoilgams question.

No. You can't do that. That's circular proving...

Do you know why they are equal rather than stating the quote from the teacher/textbook?

 

[Fawun]

Re: 2012 Year 9 &10 Mathematics Marathon

@Fawun- small hint. There's more than one circle in the picture- there's the one that has its centre in the square in the middle and four quarter circles from the outside if that makes sense.

No it doesn't make sense lol. Are you saying that the shaded area form a circle?

 

[kev-]

Re: 2012 Year 9 &10 Mathematics Marathon

you're trying to prove that Fawun.. HAHA
Draw a perpendicular line from A to line BC. Then prove RHS, so corresponding angles in congruent triangles are equal.

 

[Fawun]

Re: 2012 Year 9 &10 Mathematics Marathon

No. You can't do that. That's circular proving...

Do you know why they are equal rather than stating the quote from the teacher/textbook?

?

They are equal because they're the base angles of an isosceles triangle.

 

[SpiralFlex]

Re: 2012 Year 9 &10 Mathematics Marathon

you're trying to prove that Fawun.. HAHA
Draw a perpendicular line from A to line BC. Then prove RHS, so corresponding angles in congruent triangles are equal.

More elegance needed.

 

[kazemagic]

Re: 2012 Year 9 &10 Mathematics Marathon

No it doesn't make sense lol. Are you saying that the shaded area form a circle?

i think he means colour in white parts in the middle of the square and u get a circle?

 

[SpiralFlex]

Re: 2012 Year 9 &10 Mathematics Marathon

?

They are equal because they're the base angles of an isosceles triangle.

But WHY? I don't want you to simply quote from your teacher/textbook.

 

[Fawun]

Re: 2012 Year 9 &10 Mathematics Marathon

you're trying to prove that Fawun.. HAHA
Draw a perpendicular line from A to line BC. Then prove RHS, so corresponding angles in congruent triangles are equal.

Ohhhh shiet.

I'm totes failing year 9 and 10

 

[kazemagic]

Re: 2012 Year 9 &10 Mathematics Marathon

More elegance needed.

this can be circumscribed in a circle rite?

 

[Fawun]

Re: 2012 Year 9 &10 Mathematics Marathon

But WHY? I don't want you to simply quote from your teacher/textbook.

Jesus Christ i got dis.

hold on