Equal but unspecified constraints on angles

[Anonymous]

I can put an equal constraint between two lines without having to specify either length.

I can also put an equal constraint between two angles by copying from one to the other.

But the first angle has to be constrained to a particular value.

 Is there a way to constrain the angles to be equal but otherwise unconstrained?

[TrippyLighting]

No, I don'd think so, but you can use construction geometry and other constraints to achieve the same thing.

If you can show a screenshot or screencast of what you want to do, we can recommend specifics. 

[Anonymous]

The attached file defines a triangle which is completely unconstrained,
apart from having one vertex at the origin.

I have added construction lines from the middle of each side
to the opposite vertex: these obviously do not constrain
the triangle in any way.

I have also added construction lines which bisect each angle
and reach the opposite vertex. These were more difficult
to create since there does not seem to be a way to add an "equal"
constraint between two angles without specifying the value
of one of the angles. So I had to add a few extra construction
lines so that I could use an "equal length" constraint to ensure
that the two angles either side of the angle bisector were equal.

These extra lines should, obviously, not constrain the triangle
itself in any way.

However, when I click and drag either of the non-origin vertices,
or use the "Move" command on either of them, the triangle
jumps around wildly. In particular, I cannot do a purely horizontal
or vertical move of either vertex, although this should be possible
since the triangle itself should not be constrained at all.

[TrippyLighting]

Cool. Now I know what does not work.

That does not explain how you want for this to behave. What angles to you want to be equal ? You could explain this in a hand sketch. 

[Anonymous]

I want to construct an angle bisector (three angle bisectors, to be precise). So I drew a construction line through the angle.

I want the two angles between this construction line and the lines either side to be equal.

Here is a diagram:

http://mathworld.wolfram.com/AngleBisector.html

[TrippyLighting]

You either misinterpreted what the diagram is telling you or dis not follow it.

1. Draw a triangle.

2. Draw a 3-tanget circle touching each of the 3 sides of the triangle.

3. Draw a line form each corner post to the center of that circle. Do NOTdraw that line to the center/middle of the opposing triangle edge.

These lines will bisect that angles. Always.

[Anonymous]

You know, and I know, that the three angle bisectors meet at a single point which is the centre if the inscribed circle.

But I want to produce an interactive demonstration of that fact: so I want to draw the three bisectors separately (and all the way to the opposite side of the circle) and then show that they meet at a single point.

My method of constructing the bisector should work: but does not let you drag the vertices of the triangle around (the triangle goes crazy!)

This seems to be a bug in the program.

However, your message suggested a simpler way to construct an angle bisector: draw a small circle between the lines and make it tangent to both lines. The line from the vertex through the middle of this circle is the angle bisector. So, draw the line from the vertex to the opposite side and make it coincide with the opposide side and the middle of the circle.

Doing this for all three vertices gives a triangle which can be dragged around into different shapes: demonstrating that the three angle bisectors meet at a single point. You can then add a circle at this point which is tangent to one side and see that it is also tangent to the other sides: it is the inscribed circle. Note that in theory, there is no need to constrain the diameter of the angle bisector construction circles, but I found that setting the diameter to 1mm works better than leaving them unconstrained.

The triangle still jumps around occasionally as you drag one vertex: sometimes another vertex shoots away for no reason.

[TrippyLighting]

Aha. Now I understand the purpose of what you want to do.

Well...the problem is that the current sketch solver sucks. Badly!

Even at such simple tasks. I tried to sketch something and it told me that the sketch was over constrained even though it was not.

[TrippyLighting · Accepted solution]

I've helped myself with a few construction lines. It moves rather choppy on my mid 2010 i7 iMac. Maybe it moves more fluently on your computer.

[Anonymous]

Excellent solution! It moves fairly smoothly on my 2013 macbook air. Occasionally, one or both of the arcs will flip to the outside of the triangle: this is a bug in Fusion that I have encountered before. It is very annoying when it happens on a parameterised sketch: make a small change to a parameter, and suddenly one of your centre point arcs flips over to the other side!

[Anonymous]

I found yet another way to bisect an angle: start with a three point arc, give it a fixed radius, sketch a point at the mid-point of the arc, then a line from the vertex to the opposite side. Make this line go through the mid-point you added. See the attachment for an example.

It still tends to go crazy while you are dragging the points around.