Vertical Angles

AGE = 97

CGB = 97

DHE = 94

BHF = 94

These are examples of vertical angles. In geometry you learn that all vertical angles are congruent. From this picture you can see that angle AGE=CGB. (~CB5)

Structural Vertical Angles

Vertical Angles: Two angles whose sides form two pairs of opposite rays.
Theorem 2-3: Vertical angles are congruent.

In this situation, with the beams under the overhang, angles VUW and XUY are congruent by theorem 2-3, and it is also proven through the angle measurements given by GSP. (~AI5)

Geometric Tiles

  

Tiles are often used for flooring because of the intricate patterns and tessellations that they can form. In this photo you can see examples of congruent triangles. You can tell that they are congruent because of the verticals angles and the fact that they are next to squares -- this arrangement shows the use of the SAS postulate to prove the triangles congruent. You could also use parallel lines and interior angles to use the ASA postulate. (~AL1)

Vertical Angles

Here is a great example of vertical angles being congruent. I noticed these two long diagonal poles intersecting:

I decided to take a picture of these poles intersecting to find out if the vertical angles really were congruent. Using Geometer's SketchPad, I was able to figure out that the angles were congruent, no matter how I sized the picture. 

The measures of both angles are congruent, because vertical angles are congruent. I walk past this feature every day, along with several others like it, and I can't help noticing that vertical angles are everywhere in our lives. (~DM5)