Geometry is a very multifaceted science. It 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 conclusions 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 easy to prove.
Cornering
Any angle is formed by crossing two lines or drawing two rays from one point. They can be called either one letter or three, which successively designate the points of construction of the corner.
Angles are measured in degrees and can (depending on their value) be called differently. So, there is a right angle, acute, obtuse 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 is an angle greater than 90 degrees.
An angle is called right when its measure is 90.
In thatthe case when it is formed by one continuous straight line, and its degree measure is 180, it is called unfolded.
Adjacent corners
Angles that have a common side, the second side of which continues each other, are called adjacent. They can be either sharp or blunt. The intersection of a straight 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 of them can be easily calculated if the other is known.
- It follows from the first point that adjacent angles cannot be formed by two obtuse or two acute angles.
Due to these properties, one can always calculate the degree measure of an angle given the value of another angle, or at least the ratio between them.
Vertical corners
Angles whose sides are continuations of each other are called vertical. Any of their varieties can act as such a pair. Vertical angles are always equal to each other.
They are formed at the intersection of lines. Together with them, adjacent corners are always present. An angle can be both 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 cross-lying angles. They are equal to each other. They can be viewed in light of the properties that vertical and adjacent angles have.
Sothe topic of corners seems to be quite simple and understandable. All their properties are easy to remember and prove. Solving problems is not difficult as long as the angles correspond to a numerical value. Already further, when the study of sin and cos begins, you will have to memorize many complex formulas, their conclusions and consequences. Until then, you can just enjoy easy puzzles in which you need to find adjacent corners.
