There's a script that can do this.
Scroll down this page on Design Tuts Plus to find the one named "Dup at Selected Anchors".
Download it and extract the .js file contained in the zip. Save it somewhere you can easily find it again*.
In Illustrator draw a triangle or any shape with the pen tool or a shape tool, then draw a filled small circle. Select both circle and shape. Click File > Scripts > Other script, and locate the script you saved previously, and run it.
Copies of the circle will be placed at all the anchor points of the shape
Here's an example using a star shape and a circle.
In case of link rot, here's the page on web.archive.org
*Note: Alternatively you can save the script in your Adobe Illustrator scripts folder. Then you can access it directly by going to File > Scripts, and it should be listed.