They are called Angles opposite the vertex when the sides of one are semi-straight opposite the sides of the other. The angles opposite the vertex have the property that "all the angles opposite the vertex are equal" .
This property is one of the simplest in the area of geometry, it can be used when two lines intersect. If a pair of lines intersect, it will form 4 angles less than 180º. The 4 angles are going to have a point in common which is called the vertex, at this point is where the two lines intersect. If the lines are perpendicular to each other, the four angles will be right, if the lines are not perpendicular, then two of the angles will be acute and the other two will be obtuse.
Each acute angle will have the vertex and one side in common with each of the obtuse angles; likewise, an obtuse angle will have the vertex and a side in common with each acute angle; likewise, an acute angle and an obtuse angle must add up to 180º because they have a common side and the other sides belong to the same line.
The Vertex Angles Theorem contemplates the following statement: These kinds of angles are coherent and precise. Hypothesis: Alpha and Beta opposed by the vertex. Thesis: Alpha is equal to Beta. Proof: Alpha plus Y is equal to 180º because they are adjacent; in turn, Beta plus Y is equal to 180º because they are also adjacent. As a consequence of the transitive property, the initial terms must be similar to each other, that is, Alpha plus Y is equal to Beta plus Y. therefore Y is equal to itself, subtracting it from both members of the equality. As a conclusion, it can be said that the bisectors of two opposite angles by the vertex are opposite rays.
