Linear Pair Property,
Congruent Triangles (SAS,
The situation is represented in the diagram below:
|In this example, each of the roads leading up to the intersection is one block
long. We found earlier that the angles opposite each other in the intersection
have equal measure due to the Vertical Angle Theorem. Since the
sides have equal length and the included angles are the same, the two triangles
formed, Triangle ABC and Triangle EDC are congruent
by SAS. If you think about the Parallel Line Property,
congruency could also be proved by AAS and ASA...
Note that there is a footpath that extends from vertex C down
to segment DE (in the colored diagram). This footpath actually splits vertex C
into two equal angles. This would then be called an angle bisector.
We also note that in this case the footpath bisects segment DE
at a perpendicular angle. Consequently, the footpath could also be known as a
The Linear Pair Property (LPP) is shown above as well. The
LPP simply refers to a line that is intersected by another line and creates
two angles that add up to 180 degrees. For example, angles 6 and 7
form a linear pair.