Vertical and adjacent angles

Geometry is a very versatile science. It develops logic, imagination and intellect. Of course, because of its complexity and a huge number of theorems and axioms, it is not always pleasant for schoolchildren. In addition, there is a need to constantly prove their findings, using generally accepted standards and rules.

Adjacent and vertical angles are an integral part of geometry. Surely many schoolchildren simply adore them for the reason that their properties are clear and simple in the proof.

Formation of angles

Any angle is formed by crossing two straight lines or holding two beams from one point. They can be called either one letter or three, which consistently indicate the points of the angle construction.

Angles are measured in degrees and can (depending on their value) be called differently. So, there is a right angle, sharp, blunt and unfolded. To each of the names there corresponds a certain degree measure or its interval.

A sharp angle is called a measure of which does not exceed 90 degrees.

The blunt angle is greater than 90 degrees.

The angle is called right if its degree measure is 90.

In the case when it is formed by one continuous line, and its degree measure is 180, it is called expanded.

Adjacent angles

Angles that have a common side, the second side of which continues one another, are called adjacent. They can be either sharp or stupid. The intersection of the unfolded corner by a line forms adjacent angles. Their properties are as follows:

1. The sum of such angles will be 180 degrees (there is a theorem proving this). Therefore one can easily calculate one of them if the other is known.
2. From the first point it follows that adjacent angles can not be formed by two blunt or two acute angles.

Due to these properties, you can always calculate the degree measure of the angle, having the value of another angle or, at least, the relation between them.

Vertical angles

Angles, the sides of which are continuation of each other, are called vertical angles. As such a pair can act any of their varieties. Vertical angles are always equal to each other.

They are formed when the lines intersect. Together with them there are always adjacent corners. The angle can be simultaneously adjacent to one and vertical to the other.

When intersecting parallel lines with an arbitrary line, several other types of angles are also considered. Such a line is called a secant line, and it forms corresponding, one-sided and cross-lying corners. They are equal to each other. They can be considered in the light of properties that have vertical and adjacent angles.

Thus, the theme of angles seems quite simple and understandable. All their properties are easy to remember and prove. Solving problems does not seem complicated until the corners correspond to a numerical value. Already further, when the study of sin and cos begins, it will be necessary to memorize many complex formulas, their conclusions and consequences. Until that time, you can simply enjoy light tasks in which it is necessary to find adjacent angles.