Geometry is a very multifaceted science. She develops logic, imagination and intelligence. Of course, due to its complexity and the huge number of theorems and axioms, schoolchildren do not always like it. In addition, there is a need to constantly prove their findings using generally accepted standards and rules.
Adjacent and vertical angles are an integral component of geometry. Surely many schoolchildren simply adore them for the reason that their properties are clear and easy to prove.
Cornering
Any angle is formed by the intersection of two lines or by drawing two rays from one point. They can be called either one letter or three, which successively indicate the points of construction of the angle.
Angles are measured in degrees and may (depending on their value) be called differently. So, there is a right angle, sharp, blunt and deployed. Each of the names corresponds to a certain degree measure or its interval.
An acute angle is an angle whose measure does not exceed 90 degrees.
An obtuse angle is greater than 90 degrees.
An angle is called direct if its degree measure is 90.
In the case when it is formed by one solid line, and its degree measure is 180, it is called expanded.
Adjacent corners
Angles having a common side, the second side of which extends each other, are called adjacent. They can be either sharp or dull. The intersection of the unfolded angle with a line forms adjacent angles. Their properties are as follows:
- The sum of such angles will be equal to 180 degrees (there is a theorem proving this). Therefore, one can be easily calculated if the other is known.
- It follows from the first paragraph that adjacent corners cannot be formed by two obtuse or two acute angles.
Thanks to these properties, you can always calculate the degree measure of the angle, having the value of another angle, or at least the ratio between them.
Vertical angles
Angles whose sides are a continuation of each other are called vertical. As such a pair can be any of their varieties. Vertical angles are always equal.
They are formed at the intersection of lines. Together with them are always present and adjacent corners. The angle can be simultaneously adjacent to one and vertical to the other.
When crossing parallel lines with an arbitrary line, several more types of angles are also considered. Such a line is called a secant, and it forms the corresponding, one-sided and crosswise lying corners. They are equal to each other. They can be considered in light of properties that have vertical and adjacent angles.
Thus, the theme of angles seems rather simple and understandable. All their properties are easy to remember and prove. Solving problems does not seem complicated as long as the corners correspond to a numerical value. Further, when the study of sin and cos begins, one will have to memorize many complex formulas, their conclusions and consequences. Until that time, you can simply enjoy easy tasks in which you need to find adjacent angles.