Congruent chords are equidistant from the centre of a circle
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Objectives
Understanding equal chords are at equal distance from the centre
Estimated Time
40 minutes
Prerequisites/Instructions, prior preparations, if any
Basics of circles and its related terms should have been done.
Materials/ Resources needed
- Digital : Computer, geogebra application, projector.
- Non digital : Worksheet and pencil, compass, strings
- Geogebra files : Equal chords and distance from center.ggb, Equidistantchords.ggb
This geogebra file has been created by Tharanath Achar of Dakshina kannada.
Process (How to do the activity)
Developmental Questions
- What is a chord ?
- Name the centre of the circle.
- How do you draw congruent chords in a circle ?
- How many chords do you see in the figure ? Name them.
- If both the chords are congruent, what can you say about the length of both the chords ?
- How can we measure the length of the chord ?
- What is the procedure to draw perpendicular bisector ?
- What does theorem 1 say ? Do you all remember ?
- What is the length of both chords here ?
- What can you conclude ?
- Repeat this for circles of different radii and for different lengths of congruent chords.
Equal chords and distance from center.ggb
- Two chords equal chords are at equal angles with diameter from a point on the circle.
- Identify the congruent elements for the triangles formed when perpendicular is drawn to chords from center of the circle.
- Can these equal chords be any where in the circle, then what about their perpendicular distances.
Equidistantchords.ggb
- Use the files to demonstrate equal chords are at equal distance from the center
- Show the animation by overlapping the two chords to show they are equal
- Evaluation Questions
- Were the students able to comprehend the drawing of congruent chords in a circle ?
- Were the students able to comprehend why congruent chords are always equal for a given circle. Let any student explain the analogy.
- Are the students able to understand that this theorem can be very useful in solving problems related to circles and triangles ?
- What is a chord ?
- What are congruent chords ?
- Why do you think congruent chords are always equal for a circle of given radius ?