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.

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