dropdown menu with top triangle

Question

I want to create a dropdown menu like this:

http://www.howdyjeff.com/

but I cant horizontally center the top triangle and the dropdown menu (based on the li a) and I'm having some :hover problem, because the dropdown ul fades away.

how can I do that?

JSFiddle:

https://jsfiddle.net/zw5rqzut/

html {
    text-align: center;
}
nav {
    width: 100%;
    height: auto;
    background-color: #000;
}
ul li {
    display: inline-block;
    position: relative;
    margin: 1em
}
ul ul {
    display: none;
    position: absolute;
    background-color: #000;
    top: 50px;
}
ul ul:after {
    position: absolute;
    left: 50%;
    top: -8px;
    width: 0;
    height: 0;
    content: '';
    border-left: 20px solid transparent;
    border-right: 20px solid transparent;
    border-bottom: 20px solid #000000;
}
a {
    color: #fff;
    text-decoration: none;
}
li:hover ul {
	display:block;
}

<nav>
    <ul>
        <li>
            <a href="#">Dropdown1</a>
            <ul>
                <li><a href="#">Option1</a></li>
                <li><a href="#">Option2</a></li>
                <li><a href="#">Option3</a></li>
            </ul>
        </li>
        <li>
            <a href="#">Dropdown2</a>
            <ul>
                <li><a href="#">Option1</a></li>
                <li><a href="#">Option2</a></li>
                <li><a href="#">Option3</a></li>
            </ul>
        </li>
        <li>
            <a href="#">Dropdown3</a>
            <ul>
                <li><a href="#">Option1</a></li>
                <li><a href="#">Option2</a></li>
                <li><a href="#">Option3</a></li>
            </ul>
        </li>
    </ul>
</nav>

Answer 1

To center the triangle horizontally, simply use transform as below:

left: 50%;                     //as you did
transform: translateX(-50%);