1.10. Vertical Angles http://www.ck12.org
1.10 Vertical Angles
Here you’ll learn about vertical angles and how they can help you to solve problems in geometry.
What if you want to know how opposite pairs of angles are related when two lines cross, forming four angles? After
completing this Concept, you’ll be able to apply the properties of these special angles to help you solve problems in
geometry.
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Click image to the left for more content.CK-12 Foundation: Chapter1VerticalAnglesA
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Click image to the left for more content.James Sousa:Vertical Angles
Guidance
Vertical anglesare two non-adjacent angles formed by intersecting lines. In the picture below,^6 1 and^6 3 are vertical
angles and^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: 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.