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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