Augmentation dots and tenuto ties are two types of markings used to alter a note's duration.
A dot increases duration by one half.
Since an eighth note is half the duration of a quarter note, we will substitute it for the 1/2 symbol.
As you can see, a dotted quarter note is equal to a quarter note plus an eighth note.
A dotted quarter note can also equal three eighth notes.
Ties merge multiple notes of the same pitch.
They are used to let the duration of a note travel across barriers (such as the measure line in this example).
The fourth and fifth notes are now combined. If the measure line were not there, we could have written a half note instead.
Use this chart for reference to augmentation dots.