Investigating Properties of Chords and Arcs

Objective:  Have students understand four theorems concerning properties of chords and arcs of circles.


Lesson:

Have the students perform some investigations in GSP to help them deduce some theorems about chords of circles.  These theorems are as follows:

Theorem 1:  In a circle, or in two congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

mAOC = mBOC if and only if mAB = mBC

Theorem 2:  If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

If m<ODB = 90o, then mAD = mDB

Theorem 3:  If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.

If mAB = mBC then m<OBC = 90o

Theorem 4:  In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

mDC = mAB if and only if mOE = mOF.
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For the GSP activity, click here.  Here are the GSP sketches:  Theorem 1, Theorem 2, Theorem 3, Theorem 4.



Conclusion:  Discuss the theorems the students discovered, what conclusions they were able to form from the activities.



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Developed by Katherine Huffman