Type of Class: Standard High School Geometry

 Related VA SOL: G.3

 Time Frame: Ninety minute block class

 Objectives:

• Students will know the definition of a transversal line.
• Students will know the definitions of alternate interior angles, same-side interior angles, and corresponding angles.
• Students will apply knowledge of parallel lines and transversals and apply them to practical problems.

Materials:

• Geometer’s Sketchpad
• Chalkboard
• Handout

 Procedure:[1]

1)      Definition

a)      Transversal: A line (or segment) that intersects two coplanar lines (or segments) at two distinct points.  The diagram below shows the eight angles formed by the transversal and two segments.

i)  and  are in the interior of l and m. 

·        Name another pair of interior angles.

·          and  are alternate sides of the transversal t.

·        Name another pair of angles on alternate sides of t.

·        Name a pair of angles on the same side of t.

2)      Sketchpad to be done in groups of 3 or 4 selected at teacher’s discretion.

a)      Construct two parallel lines (or segments) and have them intersected by a transversal line (or segment).

b)      Label all points (for example)

i)        Measure all eight angles created by the transversal.

ii)       Rotate the transversal by moving it with points E or F (for example).

·        Repeat this rotation two more times, recording the angle measurements for each.

c)      Have the groups form a conjecture concerning:

i)        Corresponding angles

ii)       Alternate interior angles

iii)     Same-side interior angles

d)      Have each group read their conjectures aloud.

i)        The class will then form a class-wide conjecture regarding corresponding, alternate interior, and same-side angles.

e)      In case the class has a hard time coming together for one concise conjecture for each of the three angles

•  Please refer to the diagram below.

i)        Corresponding angles: If two parallel lines are cut by a transversal, then corresponding angles are congruent.

·        If l is parallel to m, then .

ii)       Alternate Interior angles: If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

·        If l is parallel to m, then  and .

iii)     Same-side Interior Angles: If two parallel lines are cut by a transversal, then pairs of same-side interior angles are supplementary.

·        If l is parallel to m, then  and  are supplementary, and so are

                   and .

3)      Examples to be done as a class together:

Assessment: Problems 3 and “Measuring Earth” from above.

 Suggestions/Comments: This activity would best be carried out in a computer lab.  This way, the students can do their group work at a computer station to lesson the time of students moving around the room.