Geomerty question
 

http://i139.photobucket.com/albums/q...ela88/psu2.jpg
The black dot is the centre of the circunference btw.

Is the blue angle equal to the sums of the green angle and the red angle? My textbook says it is but I dont see how can that be? [img]/images/graemlins/frown.gif[/img]

Re: Geomerty question
 

Level?

Re: Geomerty question
 

no...but now I know why the blue angle = red + green

Re: Geomerty question
 

Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )

So we require to show that the blue angle = the pink angle + the green angle . But this follows from the exterior angles theorem .

Re: Geomerty question
 

[ QUOTE ]
Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )


[/ QUOTE ]

Green and pink are not necessarily equal.

You meant to say:

Angle green = angle yellow since they are subtended by the same chord.


So it is sufficient to show that blue = yellow + red.

Z

Re: Geomerty question
 

[ QUOTE ]
[ QUOTE ]
Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )


[/ QUOTE ]

Green and pink are not necessarily equal.

Z

[/ QUOTE ]

I think it's clear when I say that the angles are equal because it is subtended by the same chord . It is very easy to show that blue = yellow + red since the sum of the angles of a triangle is 180 .

Re: Geomerty question
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )


[/ QUOTE ]

Green and pink are not necessarily equal.

Z

[/ QUOTE ]

I think it's clear when I say that the angles are equal because it is subtended by the same chord . It is very easy to show that blue = yellow + red since the sum of the angles of a triangle is 180 .

[/ QUOTE ]

You wrote angle green = angle pink.
That statement is false. Although you give the explanation about angle green and angle yellow opening the same chord, hence angle green = angle yellow. And now you can say angle blue = angle yellow + angle red

Re: Geomerty question
 

Hmm, it's clear that:
g+p=b

and

y+r=b

But, I don't know how to get b=g+r

Re: Geomerty question
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Angle green = angle pink since it is subtended by the same chord . (ie , the chord formed from the vertices of the green angle and yellow angle )


[/ QUOTE ]

Green and pink are not necessarily equal.

Z

[/ QUOTE ]

I think it's clear when I say that the angles are equal because it is subtended by the same chord . It is very easy to show that blue = yellow + red since the sum of the angles of a triangle is 180 .

[/ QUOTE ]

You wrote angle green = angle pink.
That statement is false. Although you give the explanation about angle green and angle yellow opening the same chord, hence angle green = angle yellow. And now you can say angle blue = angle yellow + angle red

[/ QUOTE ]

It was a typo . Thx for clearing that up .

Re: Geomerty question
 

These types of problems are very simple. Ignore the circle in the beginning. Two properties are used:
1.) Two angles forming a straight angle are supplementary angles. Basically this means when there are two angles side by side on a straight line, they add up to 180 degrees.
2.) The 3 angles on a triangle add up to 180 degrees.

The rest is just algebra. Label each relevant angle x, y, z, etc. Write out relationships that you find. Combine equations to show your desired equality.