Type of Class:
             Standard High School Geometry

Related VA SOL: G.3

 Time Frame:
         Ninety minute block class

Objectives:

• Students will know the terms complementary, supplementary, and vertical angles.
• Students will apply knowledge of complementary, supplementary, and vertical angles to solve problems.

Materials:

• Geometer’s Sketchpad
• Overhead
• Straws (3 per group)
• Paperclips
• Protractor

Procedures:

1)      Vertical Angles

a)      Students will be placed into groups of 2-4 students.  In these groups, the students will be given three straws, one paperclip, and a compass.  They will lay one straw over another and clip the center of the two straws, thus forming vertical angles (with the clip as the point of intersection). 

b)      Students will measure all angles formed by the intersection.

c)      Students will label each angle  and write down the measure of each angle.

d)      After recording the measurements, the students will move the straws around to repeat the activity 5 times.

i)        Each group will form a conjecture about vertical angles based on what they have observed.

• Given two nonadjacent angles formed by two intersecting lines/rays/segments,  and  have the same angle measurement. 

       and  have the same angle measurement

e)      Students will go to the computer and open up a new Geometer’s Sketchpad sketch window.

i)        Students will construct two intersecting lines and measure the four angles.

ii)       Keeping the angle measurements on the screen, students will then drag the resulting endpoint of one line segment and move it around clock-wise and observe how the angle measures change with respect to each other.

iii)     They will then drag the other line and move it around counter-clockwise and observe how the angle measurements change in relation to each other.

iv)     This should verify their conjecture from above.  If it does not, they should now form a new conjecture.

2)      Supplementary Angles

a)      Students will now go back to their straws and measure two angles that are not vertical and record their measurements.

i)        Students will then move the straws around and record more measurements.

ii)       Students will then form a conjecture based on their observations.

b)      Students will return to Geometer’s Sketchpad

i)        Students will open a new window and construct two intersecting lines and measure the two adjacent angles.

• Leaving the angle measures on the screen, the student will then drag one line around and observe how the two angles relate to each other.

ii)       Students will now verify the conjecture from above.  If it does not match, they should form a new one.

3)      Class-wide conjecture

a)      Once all the groups are finished with both parts of the activity, the class will come together and form two concise conjectures regarding vertical and supplementary angles.

i)        Note: The teacher should now provide the class with the terms vertical and supplementary angles and also present formal definitions.

b)     Provide students with examples of complementary angles and have the come up with a definition.

4)      Questions to be placed on the overhead

a)       

_____________________________________________________________________

b)       

 _____________________________________________________________________

c)

_____________________________________________________________________

d)

Assessment: Solve four problems 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.  Teacher demonstration of the straw and Sketchpad activity before hand would also expedite the lesson and cause less confusion.  A worksheet to go along with the lesson would be preferable, but not necessary.