Activities Involving Parallel Lines
Objective: Students will be able to identify parallel lines.
Activity-Have students think of games that they play with family members, either at home or elsewhere, that make use of parallel lines. For example, most court and field games, such as tennis, basketball, and soccer, use parallel lines to form the boundaries of the playing field. Also, many board games use parallel lines, as do playing cards. Tell students to think of as many games as they can and provide a brief written description or sketch to describe how parallel lines are used in each game.
Activity-Ask pairs of students to model parallel, intersecting, and skew lines in various ways around the room. For example, the pair could stand against the same wall parallel to each other to model parallel lines, or one could stand leaning slightly to model intersecting lines. Ask for volunteers to display their line models to the class.
Objective: Students will be able to identify exterior, interior, corresponding, alternate interior, and supplementary angles.
Activity-Students will make three-dimensional models of parallel lines with transversals. They can paste their models on poster board and label the angles. Suggest that students use such materials as drinking straws, craft sticks, and pipe cleaners to make their models.
Activity-Have students find an object at home that models a transversal intersecting two or more lines, such as a rung and the legs of a chair. Ask students to make a simple sketch of the object, highlighting the transversal and the lines it crosses, and then name the various pairs of angles that are formed. Also, have students estimate the measures of the different angles both in the actual object and in their drawing to check the accuracy of their sketch. Students should also identify pairs of angles that should be supplementary.
Activity-Ask groups of three or four students to draw five sets of lines being cut by a transversal. Instruct them to draw the first four sets with nonparallel lines crossed by a transversal, with each set getting closer to being parallel. The fifth set should be parallel lines crossed by a transversal. Ask them to number the sets 1 to 5. Have students measure the same pair of alternate interior angles to find the sum of the same-side exterior angles in each set of lines and to record their data in an organized chart. After reviewing and discussing the data in their chart, students should draw conclusions about the measures of alternate interior angles and the sum of same-side exterior angles for lines that are not parallel and lines that are parallel.
Objective: Students will use theorems and definitions to find the measures of angles.
Activity-Tell students to draw two identical sets of parallel lines cut by a transversal (not perpendicular to the parallel lines) large enough so that they can cut the angles out, and then label each set of eight angles a, b, c, d, e, f, g, h. Have students cut the angles out of one drawing and find and record all the pairs of angles that are congruent or supplementary. They can compare their findings to the angles in the uncut set of lines to verify the theorems presented in the lesson.
Activity-Have students draw sketches and write statements on index cards to identify the theorems, and other axioms, definitions, and properties they need to review. For example, they might draw parallel lines with alternate interior angles labeled x and y and write the statement m<x = m>y. Working with a partner, one student holds up a card and the other recites the theorem, property, etc., that justifies the statement on the card. Students can take turns holding the cards and reciting the theorems.
Activity-Have students find and research a specific job or occupation in which proofs and deductive reasoning are used either directly or indirectly by persons working in the field. Brainstorm a list of occupations with the group-scientists such as chemists, physicists, or geologists and medical personnel such as doctors, paramedics, and lab technicians. Tell students to describe the job or occupation and explain how proofs are used and by whom.
Objective: Students will be able to use the converse of a theorem to construct parallel lines.
Activity-Have students contact a carpenter or stonemason to discuss something that he or she built that required verifying that two lines or planes were parallel or two angles were congruent. Ask students to provide a description of the project, identification of the builder, and the method the builder used to verify parallelism or congruence. Invite students to share their findings with the class.