b. An angle is ordinarily thought of as being formed by the junction of two straight lines that
may or may not continue beyond the junction. If the lines do continue, then the two opposite angles at
the vertex are known as vertical angles. This situation was illustrated in Figure 3-7. When the two lines
intersect each other at 90, then four equal angles are formed and are known as right angles. The two
right angles sharing a common side and vertex are known as supplementary angles. The opposite or
exterior sides of the two right angles form what is known as a straight angle. Each pair of right angles,
sharing a common side, can also be called adjacent angles.
c. To solve many of the geometric problems, certain principles have to be taken as they stand
and without proof . Based on personal observation, these principles or postulates should be firmly fixed
in your mind. There are 25 postulates in all, and they are listed in paragraph 3-6. To aid you in
analyzing geometric problems, you can use the superposition method, which allows you to compare by
superposition two lines, angles, or figures to determine whether they are equal or congruent.
d. Solving geometric problems is largely based on using theorems and corollaries. The latter
term refers to a secondary rule whose truth can be readily derived from a theorem. For convenience, the
theorems that are commonly used in plane geometry have been grouped together. Thus, the previous
text includes eight theorems which are essential to solving problems that involve lines and angles.
These eight theorems are listed under paragraphs 3-9 and 3-10; other theorems that aid in solving
triangles are given in paragraphs 3-11 through 3-16.