Reasoning and Parallel Line
Reasoning and Parallel Line
Reasoning and Parallel Line are as follows, There are two types of Reasoning.
1. Inductive reasoning
The process of observing, recognizing patterns, and making conjectures about the observed patterns is called Inductive reasoning. It is used commonly outside of the Geometry classroom.
2. Deductive reasoning
The process of reasoning logically from given statements to make a conclusion is called deductive reasoning. It is the type of reasoning used when making a Geometric proof. The reasoning that you use to decide whether two lines are parallel based on knowing whether corresponding angles or alternate interior angles are congruent is called deductive reasoning.
Parallel Line
Lines are parallel if they are always the same distance apart called equidistant and they will never meet.
How do we use parallel lines in coordinate geometry?
When the graphs of two linear equations are parallel in coordinate geometry, the two equations do not share a solution and the slopes of two parallel lines are equal in coordinate geometry.
Transversal line
The lines that cross two or more lines are known as the Traversal line. The Figure shows how a transversal line cuts a pair of parallel lines. When a transversal line cuts a pair of parallel lines, different pairs of angles are formed. These angles are used to prove whether two lines are parallel to each other
Properties of parallel line
When a transversal line cuts two lines, the properties below will help us determine whether the lines are parallel.
1. Corresponding angles
Two lines cut by a transversal line are parallel when the corresponding angles are equal and the two pairs of angles shown above are examples of corresponding angles. In general, they are angles that are in relative positions and lying along the same side.
2. Alternate interior angles
Alternate interior angles are equal when two lines cut by a transversal line are parallel and alternate interior angles are a pair of angles found in the inner side but are lying opposite each other.
3. Alternate exterior angles
Alternate exterior angles are equal when two lines cut by a transversal line are parallel and Alternate exterior angles are a pair of angles found on the outer side but are lying opposite each other.
4. Consecutive interior angles
If Two lines cut by a transversal line are parallel then the sum of the consecutive interior angles is and Consecutive interior angles are consecutive angles sharing the same inner side along the line.
5. Consecutive exterior angles
If Two lines cut by a transversal line are parallel then the sum of the consecutive exterior angles is Consecutive exterior angles are consecutive angles sharing the same outer side along the line.
Also, read Right Triangle Trigonometry