Download Exploring Angle Pairs

Project AMP
Dr. Antonio Quesada – Director, Project AMP
I. 2.2 Exploring Angle/Pair Relationships
(This lesson will address finding
Vertical Angles and Supplementary Angles.)
Amy Pullen
Chris Scantland
Knowledge: Students should have some familiarity using Cabri software on the
computer.
NCTM Standards met: Strand 3: Geometry and Spatial sense. Specify locations and
describe spatial relationships using coordinate geometry and other representational
systems. Draw geometric objects with specified properties, side lengths and angle
measures. Use visual tools such as networks (Cabri) to represent and solve problems.
Objectives:
*Students will create intersecting lines to discover and measure angles using
Cabri software.
*Students will make assumptions about these angles created.
*Students will attempt to define these angles using the new knowledge gained.
Materials:
This worksheet, computer, and Cabri software.
Procedures:
a. Angles and how they relate to each other.
b. Students will be in partners on one computer.
c. (Forms of assessment)
- Print finished construction, Observation of students at work, Collect worksheet,
and Discuss findings as a class.
Students should know how to create lines, segments, perpendicular lines, and
measure angles using the Cabri tools
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Name: ___________________
___________________
LAB I. 2.2
Exploring Angle/Pair Relationships
Goal 1: You will create intersecting lines to discover relationships between the
vertical and adjacent angles.
Investigate using Cabri Geometry II
1. Draw a line. Label two points X and Y on the line.
(Line tool)
2. Draw a second line that intersects the first line. Label two points A and B on
that line.
(Line and point tool)
3.
Make a point at the intersection and label it E.
(Point tool)
4. Measure the four angles formed by the intersecting lines. (Remember: when
measuring angles, select the points in order, with the vertex as the second
point.) Record the measures.
(Measuring tool)
∠YEA
∠XEA
∠BEX
∠YEA
5. What kind of angle relationship can you see
From this observation? ____________________________________________
6. Now, grab one of the lines and move it. What do you observe?
_______________________________________________________
7. Do you observe the same relationship between the angle measurements as in
number 5?
____________________________________________________________
Discussion as a class: Review what was discovered. What would you consider the
definition of vertical angles?
Goal 2: You will calculate the sum of two sets of angles and observe how they are
related.
(Using the same diagram as Goal 1)
Project AMP
Dr. Antonio Quesada – Director, Project AMP
1. Calculate the sum of the measures of any two adjacent angles. (Calculate tool)
∠BEY + ∠BEX = ______
∠YEA + ∠XEA = ______
∠BEY + ∠YEA = ______
∠XEA + ∠ XEB = _______
2. What did you observe? ____________________________________________
3. Grab a line and move the angles until they are all congruent to each other.
They equal ____ degrees. You have created perpendicular lines!
4. Delete the previous angle measures.
5. Draw another line through point E as shown.
Place points on opposites sides of point E,
Label them point G and point H.
(Line and point tool)
6. Measure these new angles you have created.
(Measuring tool)
∠AEG
∠GEY
TOTAL
7. What was observed?
______________________________________________
8. Now, grab the line with points G and H on it, and move it with in
∠AEY and ∠ XEB . What do you observe?
_______________________________________________________
(Arrow tool)
9. Do the sums remain constant no matter where you move the line with in the
specified angles? ________
10. Now measure these angles:
∠ BEH
∠ HEX
TOTAL
11. What is your final observation?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
Review: Students should be able to define vertical and supplementary angles.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Extension: Students will revisit the previous drawing in question 4 and will move GH
outside of the specified angle. They should see if the results would be the same.
1. Grab GH and move it beyond the
∠ XEB and ∠YEA . Record the new measurements.
(Pointer and measurement tool)
∠AEG
∠GEY
TOTAL
∠ BEH
∠ HEX
TOTAL
suuur
2. Were the results the same as in questions 6 and 10, when you grabbed GH and
moved it beyond ∠ XEB and ∠YEA ? Why or Why not?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________