2.3 Parallel and Perpendicular Lines
Lines and Angles
Marking the Diagram –Sometimes students confuse the marks for parallel and congruent. When introduction
them to the arrows that represent parallel lines, review the ticks that represent congruent segments. Seeing the two
at the same time helps avoid confusion.
When given the information that two lines or segments are perpendicular, students don’t always immediately see
how to mark the diagram accordingly. They need to use the definition of perpendicular and mark one of the right
angles created by the lines with a box.
Symbol Update –Students should be keeping a list of symbols and how they will be used in this class in their
notebooks. Remind them to update this page with the symbols for parallel and perpendicular.
Construction –The parallel and perpendicular line postulates are used in construction. Constructing parallel and
perpendicular lines with a compass and straightedge is a good way to give students kinesthetic experience with these
concepts. Construction can also be done with computer software. To construct a parallel or perpendicular line the
student will select the line they want the new line to be parallel or perpendicular to, and the point they want the new
line to pass through, and chose construct. The way the programs have the students select the line and then the point
reinforces the postulates.
Additional Exercises:
- Write a two-column proof of the following conditional statement.
IfABis perpendicular toBC, triangleABCis a right triangle.
Answer:
TABLE2.2:
Statement Reason
ABis perpendicular toBC Given.
<Bis right Definition of perpendicular.
triangleABCis a right triangle Definition of right triangle.Parallel Lines and Transversals
The Parallel Hypothesis –So far seven different pairs of angles that may be supplementary or congruent have been
introduced. All seven of these pairs are used in the situation where two lines are being crossed by a transversal
forming eight angles. Some of these pairs require the two lines to be parallel and some do not. Students sometimes
get these confuse on when they need parallel lines to apply a postulate or theorem, and if a specific pair is congruent
or supplementary. A chart like the one below will help them sort it out.
Chapter 2. Geometry TE - Common Errors