Building double angles in isosceles triangle by compasses and striaghtedge

shahar

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The question is:
Build by compasses and straightedge so the vertex angle will be double of the base angle.

please show how to do or website that show hints or solution to the question.
 
The question is:
Build by compasses and straightedge so the vertex angle will be double of the base angle.

please show how to do or website that show hints or solution to the question.

I would start by using simple algebra to determine what the angles will be. (The answer is very simple.) Then you should recognize (or look up) how to construct a triangle with those angles.

Start with the fact that the sum of the interior angles of a triangle is 180 degrees.

If you need help with this, please be specific about what you know about constructions, and what you have done to find the angles.
 
...what you have done to find the angles.
I think to draw a circle so I can create the two equal sides of the triangle. Now, what is next?
The radii of the circle will be the sides.
 
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I think to draw a circle so I can create the two equal sides of the triangle. Now, what is next?
The radii of the circle will be the sides.

I suggested working out the angles before starting to draw. But you can also start by planning the construction.

You might imagine what the triangle will look like. Without trying to do an actual construction yet, sketch an isosceles triangle, and draw in the bisector of the apex (vertex) angle. Since that apex angle is twice either base angle, how will its two halves compare to the base angles?
 
I suggested working out the angles before starting to draw. But you can also start by planning the construction.

You might imagine what the triangle will look like. Without trying to do an actual construction yet, sketch an isosceles triangle, and draw in the bisector of the apex (vertex) angle. Since that apex angle is twice either base angle, how will its two halves compare to the base angles?
I divide It to two triangles.
The triangle have:
By your hints I calculate the angles. They are: 45, 45, 90 degrees each one.
x = base angle
2x = vertex angle
x + 2x + x = 180
4x = 180
=> base(s) angle = 45, vertex angle = 90.
O.K. How it combine to one full solution?
 
I divide It to two triangles.
The triangle have:
By your hints I calculate the angles. They are: 45, 45, 90 degrees each one.
x = base angle
2x = vertex angle
x + 2x + x = 180
4x = 180
=> base(s) angle = 45, vertex angle = 90.
O.K. How it combine to one full solution?

You have found the angles by two different methods. There is no need to combine them; just choose your favorite.

But you now have to construct the triangle, which can be done by any of various standard methods.
 
Do you know how to draw a right angle?

You can start by drawing any straight line with your straightedge. Then using your compass you can draw the perpendicular line to this line. Do you know how to do that? If not, then please ask for help. If you can, then how would you complete the triangle?
 
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