http://www.ck12.org Chapter 1. Basics of Geometry
So, plug inqto get the measure of each angle.
m^6 ABD= 7 ( 22 ◦)− 46 ◦= 108 ◦ m^6 DBC= 180 ◦− 108 ◦= 72 ◦Example 6:Are^6 CDAand^6 DABa linear pair? Are they supplementary?
Solution: The two angles are not a linear pair because they do not have the same vertex. However, they are
supplementary, 120◦+ 60 ◦= 180 ◦.
Vertical Angles
Vertical Angles:Two non-adjacent angles formed by intersecting lines.
(^6) 1 and (^6) 3 are vertical angles
(^6) 2 and (^6) 4 are vertical angles
Notice that these angles are labeled with numbers. You can tell that these are labels because they do not have a
degree symbol.
Investigation 1-5:Vertical Angle Relationships
- Draw two intersecting lines on your paper. Label the four angles created^61 ,^62 ,^63 ,and^6 4. See the picture
above. - Take your protractor and findm^6 1.
- What is the angle relationship between^6 1 and^6 2? Findm^6 2.
- What is the angle relationship between^6 1 and^6 4? Findm^6 4.
- What is the angle relationship between^6 2 and^6 3? Findm^6 3.
- Are any angles congruent? If so, write down the congruence statement.
From this investigation, hopefully you found out that^61 ∼=^6 3 and^62 ∼=^6 4. This is our first theorem. That means it
must be proven true in order to use it.