Symmetries of a Circle

PROPERTY 1A

Draw a chord for circle A. Construct the perpendicular bisector of the chord. Move the chord, paying attention to the perpendicular bisector.

CONJECTURE:

The perpendicular bisector of a chord always goes through what point of the circle.

PROPERTY 1B

Construct a diameter of the circle. Draw a chord such that it is perpendicular to the diameter. Find the lengths of each segment of the chord. Move the chord, paying attention to the lengths of each segment of the chord.

CONJECTURE:

If a diameter is perpendicular to a chord then the diameter will __________________. (complete the statement)

PROPERTY 2

Find the length of each chord to the centre of the circle.

CONJECTURE:

If two chords of a circle are of the same length then what conclusion can we make?

APPLICATION: Points C, D, and E represent three apple trees in a yard. Where would you place a sprinkler so that the trees are equidistant from the sprinkler? Label the sprinkler clearly.

Symmetries of a Circle

PROPERTY 1A

CONJECTURE:

PROPERTY 1B

CONJECTURE:

PROPERTY 2

CONJECTURE:

APPLICATION: Points C, D, and E represent three apple trees in a yard. Where would you place a sprinkler so that the trees are equidistant from the sprinkler? Label the sprinkler clearly.

Information: Symmetries of a Circle