Download Using the ClassPad and Geometry

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Transcript
Using the ClassPad’s Geometry within eActivity
This activity gives step by step instructions on how to explore the
relationship of the angle formed by a tangent to a circle with a chord and
the arc angle of the chord.
Goal – to have students understand the relationship between the angles
formed by a tangent to a circle with a chord and the arc angle of the chord.
Students will discover the missing word in the statement:
The angle formed by a tangent and a chord is equal to ________ the
measure of the intercepted arc.
To begin, select
eActivity.
If your eActivity
window is cluttered,
select File then New.
Select OK!
In the steps that follow, we will:
• Draw a circle
• Draw a tangent to the circle
• Draw a chord
• Draw radii
• Measure angles
• Create an animation
Casio Education Technology M.R.D. Center
Portland, Oregon
1
1st
We need to insert a
Geometry strip into our
eActivity window.
•
Open the Insert
menu
•
Select Geometry
2nd
Draw a circle
•
Select
(circle icon)
•
Tap the Geometry
window twice
•
Or, you can tap once,
release, then drag
First tap a
center point.
Second
tap…
3rd
Draw a tangent to the
circle:
•
(tangent to
Select
curve icon)
•
Tap a point on the
circles circumference
Casio Education Technology M.R.D. Center
Portland, Oregon
2
4th
Draw a chord:
•
(line
Select
segment icon)
•
Tap the tangent point
(pt C) to start the
Tap here to
chord
start segment.
•
Tap another point on
the circle to end the
chord
Tap here to
end segment.
5th
Draw two radii to form
arc angle CAD:
•
Tap the tangent point
and then the circles
center
•
Tap the other end of
the chord and then
the circles center
6th
Measuring angles:
•
Tap (to advance the
toolbar)
•
Select the chord and
tangent line by tapping
on them
•
Select the wrong thing?
Just tap in an empty
space to deselect
everything and try
again!
Tap here…
Casio Education Technology M.R.D. Center
Portland, Oregon
3
7th
Working with the angle measure in eActivity:
• Tap in the measurement box to select the angle measure
•
Tap and hold the selected number, then drag it to the eActivity window
•
When you see the cursor blinking in eActivity, drop the number
•
Input a division symbol following the number (tap the
hard key)
Drag right to this spot.
When you see the cursor
blinking, let go!
8th
Now we need to measure the arc angle:
• Select the arc angle and drag its measure to the eActivity window
•
Drag its measure to the eActivity window
•
Change to the math input mode (tap
•
Press EXE or tap
and select
)
to display your answer as a decimal
Nice number?
Maybe…
Casio Education Technology M.R.D. Center
Portland, Oregon
4
9th
Is there a pattern?:
• Select point D and drag it to another location on the circle
•
Measure the tangent/chord angle and then the arc angle
•
Press EXE or tap
to display your answer as a decimal
10th
Fill in the blank:
The angle formed by a tangent and a chord is equal to ________ the
measure of the intercepted arc.
Fun Bonus…
Animate point D around the circle and view many angle measures in a table.
• Select your circle and
point D
• Select Edit, Animation
and then Add Animation
Casio Education Technology M.R.D. Center
Portland, Oregon
• Select Edit, Animation and
then Go (once)
5
• Advance the toolbar
(tap ). You can also
tap
to resize.
• Select the tangent
chord angle and
then tap
.
• Select the arc angle
and then tap
. Nice
relationship!
Optional…
Can you find a relationship between the angle formed by two intersecting
secants and the arc lengths they intersect? I guess this should be another
activity, but here is a start…
Casio Education Technology M.R.D. Center
Portland, Oregon
6