How to draw a triangle within a polygon

For my part you are welcome, Rebecca.

I meant it when I said at least three.

You can also, just based on the original set of hexagon and triangle (with Round Corners, of course):

1) Create the hexagon and rotate it by 30 degrees,

2) Create a triangle with the same Radius and snap its top Anchor Point to the top Anchor Point of the hexagon,

3) Copy the triangle from 2) and lock either, then (with the other one selected) Object>Path>Add Anchor Points, then deselect and DirectSelect the new middle Anchor Points (avoiding the hexagon centre if it is set to show, you can Click or Click Drag over each; if it is hidden you can just ClickDrag over all three middle Anchor Points), then Object>Path>Average (with Both ticked), then unlock the other triangle.

You're welcome, Rebecca.

I keep finding new ways to do this:

1) Using the Line Segment Tool or the Pen Tool, connect two points skipping one between, and the same first point to the center point.

2) With both line segments from step 1 selected, click the center point with the Rotate Tool.

3) Click and hold on one of the endpoints of the longer selected line, hold down the opt/alt key, and drag in either direction around the hexagon, bypassing the first vertex and connecting to the second.

4) Press cmd/ctrl + D to repeat the rotation and duplication of the two lines.

Since you already have a usable answer, this is just for fun.

Peter

Rebecca,

Illy (job description Adobe Illustrator) can always do things in at least three ways, and she likes to play with them.

You can also (Smart Guides and Show Center (Attributes panel) are your friends):

1) Create the hexagon and rotate it by 30 degrees,

2) Create a triangle with the same Radius and snap its top Anchor Point to the top Anchor Point of the hexagon,

3) Click the hexagon so its centre shows, then

a) Press the P key and click the centre and one corner, then repeat for the other two, or

b) ClickDrag with the Line Segment Tool from the centre to each corner.

I would suggest the next way:

1. Draw a hexagone and rotate it to set sides vertical.

2. Duplicate it (Ctrl+C > Ctrl+F) and delete the needless points using Pen tool (Pen-).

3. Select all and click Divdie button in Pathfinder panel. Ungroup.

Now you can delete the main triangle if you don't need it anymore.

4. Duplicate the external triangles (Ctrl+C > Ctrl+F) and reflec them using Reflect tool. Set the axis for each reflection as the respective main triangle side.

For the best appearance set rounded corners in Stroke panel.

I added here some coloring to show the result better.

Actually, something more like the way you would do it on paper might be easier. Here's a possible way, using Smart Guides to help you:

1) After drawing the hexagon with the Polygon Tool, select the Line segment Tool and And draw between alternate corners to make the equilateral triangle shape. Smart Guides will show you when you're exactly on each corner.

2) Still with the Line Segment Tool, draw a line from each vertex of the triangle to the opposite corner of the hexagon.

3) Select one of the paths from step 2, then choose the Scissors Tool, and when Smart Guides shows that the tool is over the intersection of the three lines, click to cut, select the portion of the line that you don't want, and delete it. Repeat with the other two paths.

4) You should be left with the design you want.

Peter