Bisecting Chords with Perpendicular Diameters
Bisecting Chords with Perpendicular Diameters
Observe how a diameter perpendicular to a chord divides both the chord and its arc.
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Offene Frage 1
Move the endpoints of the chord and change the radius of the circle. What do you notice about the lengths of the two parts of the chord and the two parts of the arc?
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Offene Frage 2
Does the diameter always bisect the chord and the arc, regardless of the circle's size or the chord's position?
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Offene Frage 3
When the radii are shown, what type of triangles are formed by the radii, the distance to the center, and the chord segments?
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Offene Frage 4
Which congruence criterion (SSS, SAS, HL) can be used to prove these two right triangles are congruent?
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Offene Frage 5
Based on the congruence of these triangles, how can you justify that the diameter must bisect the chord?
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