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 Post subject: Geometric proofPosted: Fri, 27 Jan 2012 02:29:52 UTC
 Senior Member

Joined: Thu, 21 Apr 2011 03:44:05 UTC
Posts: 57
Location: Depends where I am
Here is one that is puzzling me...

The Question

Prove that angle ACB = 90 degrees
(Can someone please tell me how to do degrees signs in latex please?)

Code:
C
*
*  |  *
*    |    *
*      |      *
*        |        *
*  a       |       b  *
A*____________|____________*B
O

What I have worked out so far...

1) Triangle and triangle are congruent

2) Both of the above triangles are isosceles triangles and degrees and degrees also.

Can someone please give me hint on something that can start my proof off please? Its rather frustrating as I can sortoff see how it works in my head but cannot put it into a proof...

Thanks heaps

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 Post subject: Re: Geometric proofPosted: Fri, 27 Jan 2012 06:43:42 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
garfield wrote:
Here is one that is puzzling me...

The Question

Prove that angle ACB = 90 degrees
(Can someone please tell me how to do degrees signs in latex please?)

Code:
C
*
*  |  *
*    |    *
*      |      *
*        |        *
*  a       |       b  *
A*____________|____________*B
O

What I have worked out so far...

1) Triangle and triangle are congruent

2) Both of the above triangles are isosceles triangles and degrees and degrees also.

Can someone please give me hint on something that can start my proof off please? Its rather frustrating as I can sortoff see how it works in my head but cannot put it into a proof...

Thanks heaps

Hold on, how do you know they are congruent now? Which proof of congruence are you using? All I see is that both have two consecutive sides the same, which is not enough to conclude congruence. You'd need, for example, the included angled to be the same to conclude that. Also, degrees in is given by
Code:
$$^\circ$$

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 Post subject: Re: Geometric proofPosted: Sun, 29 Jan 2012 09:24:17 UTC
 Senior Member

Joined: Thu, 21 Apr 2011 03:44:05 UTC
Posts: 57
Location: Depends where I am
Sorry, I dont actualy really know where the congruency bit came from - must have been too late at night!

I cannot see anything more to prove it, but there must be somewhere?????

Can someone please give me a hint???

Thanks alot

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 Post subject: Re: Geometric proofPosted: Sun, 29 Jan 2012 13:40:26 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6007
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
garfield wrote:
Sorry, I dont actualy really know where the congruency bit came from - must have been too late at night!

I cannot see anything more to prove it, but there must be somewhere?????

Can someone please give me a hint???

Thanks alot

What can you say about triangle ACO?

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 Post subject: Re: Geometric proofPosted: Sun, 29 Jan 2012 14:01:50 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, garfield!

Quote:

Code:
C
o
* *  *
*   *     *
*     *        *
A o * * * o * * * * * o B
O

. . lie on a circle with center and radius

is inscribed in a semicircle.

Therefore,

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 Post subject: Re: Geometric proofPosted: Sun, 29 Jan 2012 14:24:21 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6007
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
Soroban wrote:
Hello, garfield!

Quote:

Code:
C
o
* *  *
*   *     *
*     *        *
A o * * * o * * * * * o B
O

. . lie on a circle with center and radius

is inscribed in a semicircle.

Therefore,

The question is probably designed to prove semicircular arc subtends right angle, so quoting that is cheating.

_________________

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 Post subject: Re: Geometric proofPosted: Mon, 30 Jan 2012 03:03:16 UTC
 S.O.S. Oldtimer

Joined: Fri, 27 Jul 2007 10:17:26 UTC
Posts: 278
Location: Chandler, AZ, USA
If you cannot use Soroban's proof, consider this hint:

Find ,

using the fact that
.

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