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Circle geometry

Circle geometry. Exploring the properties of circles. Exploring angles in circles. Once you start playing with creating lines and angles in a circle, you can recognize some properties or characteristics that are true. T. The line segment TB has both its endpoints on the circle.

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Circle geometry

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  1. Circle geometry Exploring the properties of circles

  2. Exploring angles in circles • Once you start playing with creating lines and angles in a circle, you can recognize some properties or characteristics that are true. T The line segment TB has both its endpoints on the circle. It is called a chord. B

  3. Exploring angles in circles When an angle radiates from the centre of the circle to the edge of the circle, it is called a central angle. T C B

  4. Exploring angles in circles • An angle that is formed by two chords that share a common endpoint is called an inscribed angle T R C The arc of a circle is a portion of the circumference usually contained by two endpoints B

  5. Exploring angles in circles • Draw a large circle • Label the centre point A • Construct a chord, label it BC • Create a central angle ∠BAC • Measure this central angle • Create an inscribed angle ∠BDC • Measure this inscribed angle • How does it compare to the central angle? • Create another inscribed angle ∠BEC • Measure this inscribed angle • How does this compare to the other inscribed angle?

  6. Exploring angles in circles • What truths have you discovered? • Stating these truths in mathematical terms: • Inscribed angles subtended by the same arc are congruent. • Angles that are formed by the endpoints of an arc are called subtended angles • The measure of a central angle is twice the measure of an inscribed angle which is subtended by the same arc.

  7. Work it girls! • Textbook page 382-383 • Complete 3, 4, 5 • Page 383 • Complete 6, 7 (Hint: Pythagoras is your friend)

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