Parallel – Through a Point
Parallel – through a point
Given: Point P is off a given line
Task: Construct a line through P parallel to the given line.
Directions:
- With your straightedge, draw a transversal through point P. This is simply a straight line which runs through P and intersects the given line.
- Using your knowledge of the construction COPY AN ANGLE, construct a copy of the angle formed by the transversal and the given line such that the copy is located UP at point P. The vertex of your copied angle will be point P.
- When the copy of the angle is complete, you will have two parallel lines.
This new line is parallel to the given line.
Explanation of construction: Since we used the construction to copy an angle, we now have two angles of equal measure in our diagram. In relation to parallel lines, these two equal angles are positioned in such a manner that they are called corresponding angles. A theorem relating to parallel lines tells us that if two lines are cut by a transversal and the corresponding angles are congruent (equal), then the lines are parallel.