From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
Line x (also known as GE, ED, and GD) and w (otherwise known as BC) appear the most parallel.
Give three other names for ∠EDB.
We can name angles using the points that make up the angles. Make sure the vertex is always in the middle of the name.
Three other names for ∠EDB are: ∠GDA, ∠GDB, and ∠EDA.
Name a pair of vertical angles.
Vertical angles are opposite angles formed by intersecting lines.
∠BED and ∠GEF are vertical angles, as are ∠BEG and ∠DEF. While there are plenty of other vertical angles in the picture, they're like the horde of relatives from out of state whose names you never seem to remember. You know they're there, but just don't call them anything.
Name an angle adjacent to ∠DBC.
Adjacent means they share a vertex and a side.
The angles ∠CBA and ∠DBE are both adjacent to ∠DBC.
Are ∠EDB and ∠BED vertical or adjacent angles? Why?
What are the definitions of adjacent and vertical angles?
∠EDB and ∠BED are neither adjacent nor vertical angles. They don't share a vertex (necessary for adjacent angles) and they aren't opposite intersecting lines (the definition of vertical angles).
Is ∠ABE adjacent to ∠DBF?
What must adjacent angles share?
Yes, ∠ABE shares a vertex and a side with ∠DBF so they are adjacent.