Let’s formulate three criteria for parallelism of straight lines.
If at the intersection of two straight secant in a cross, the lying angles are equal, then the straight lines are parallel.
Let’s prove this symptom:
Let’s denote by O – the midpoint of the segment AB. Let us drop the perpendicular OH to line b and extend it to the intersection with line a.
Consider two triangles Δ OAK and Δ OBH (triangles are equal in side and two angles adjacent to it), we conclude that the angles
∠ OKA = ∠ OHB = 90 °.
Two perpendiculars to one straight line are parallel, which means a║b.
If at the intersection of two straight secant the corresponding angles are equal, then the straight lines are parallel.
If, at the intersection of two straight secant lines, the sum of one-sided angles is 180 °, then the straight lines are parallel.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.