Segments and Angles
Pacing:This lesson should take one to one and one-half class periods
Goal:The lesson introduces students to the concept of congruency and bisectors. Students will use algebra to write
equivalence statements and solve for unknown variables.
Have Fun!Have students do a call-back, similar to what cheerleaders do. You call out “AB” and students would
retort, “The distance between!” Continue this for several examples so students begin to see the difference between
the distance notation and segment notation.
This is a great lesson for students to create a “dictionary” of all the notation and definitions learned thus far. In
addition to the flashcards students are making, the dictionary provides an invaluable reference before assessments.
When teaching the Midpoint Postulate, reiterate to students that this really is the arithmetic average of the endpoints,
incorporating algebra and statistics into the lesson.
Visualization!Students have not learned about a perpendicular bisector. Have students complete Example 3 without
using their texts as guides. Have students show their bisectors. Hopefully your class will construct multiple bisectors,
not simply those that are perpendicular. This helps students visualize that there are an infinite amount of bisectors,
but only one that is perpendicular.
Fun Tip!To visualize the angle congruence theorem and provide a means of assessing the ability to use a protractor,
give students entering your class an angle measure on a slip of paper (the measurements should repeat). Have the
students construct the angle as a warm up. Then have the students find their “matching” partner and check their
partner’s angle using a protractor.
Physical Models! Once students have reviewed Example 5, have them copy the angle onto a sheet of notebook
paper or patty paper and measure the degree of the bisector. Students will construct a fold at that particular angle
measurement to see the angle bisector ray.
Real Life Application!Another method of illustrating angle bisectors is to show a compass rose, as shown below.
http://commons.wikimedia.org/wiki/File:Compass_rose_browns_00.svg
Students can see how directions such as SWS, NNW, etc bisect the traditional four-corner directions.
Angle Pairs
Pacing:This lesson should take one to one and one-half class periods
1.1. Basics of Geometry