|
Activity: Students will take
measurements of arcs and angles on designated diagrams and, with the
help of the graphing calculator, discover the formula for angles formed
by two chords intersecting inside a circle and for the angle formed by
two secants intersecting outside of the circle.
Timing:
This activity can be used prior to introducing the formulas for two
chords intersecting inside of a circle and two secants intersecting
outside of a circle. It can also be used as a follow-up to the
introduction of these formulas as reinforcement and/or verification of
the formulas.
Materials:
Protractors and rulers (the circular
protractors work well)
Worksheets (Data, Stat, Calculator)
Graphing Calculators (directions for TI-83+/84+) |
 |
Process and Handouts:
| Distribute the Data sheets
and Stat Collection sheets to students. The Data sheet will
contain the designated circle drawings involving intersecting chords and/or
intersecting secants. |
|
| Using the rulers
and protractors, students will measure the labeled angles and
their intercepted arcs. Do one of the problems orally with
the students so that they will understand how to proceed.
Have students record their findings on the Stat Collection sheet.
The Stat Collection sheet includes tables for students to
record the angles' measures, the measures of the two intercepted
arcs, and the sums and differences. |
|
After the data is gathered and
recorded, hand out the Calculator Worksheets. |
|
| Using
the directions that appear on the Calculator Worksheet, students will enter information into the
lists on the graphing calculator. List L1 will contain the angles' measures, L2 will
name the corresponding sums, L3 will contain angles' measures, and L4 will name the corresponding
differences. Students will use the stat plots and
Zoom stats to graph their data. Comparisons will be made
of L1 and L2 and then L3 and L4. The equation of the
results from LinReg(ax+b) will show that the sum (or
difference) is twice the angle. As a
result of this investigation, students will discover the
formulas for an angle formed by two chords intersecting inside a
circle and for an angle formed by two secants intersecting
outside a circle. |
|
 |
|
The arcs are measured by
measuring their respective central angles. It will be
necessary to draw the radii to the ends of each arc to form the
central angles. |
|
